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Copyright N°__1 

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OPERATOR’S HANDBOOK 



INSTRUCTIONS FOR SETTING-UP 
AND OPERATING THE FELLOWS 
SPUR AND HELICAL GEAR SHAPERS 


A Handbook for the Exclusive Use of Operators 

Comprising a Group of Printed Instructions and Suggestions Supplementing those 
Given by Our Demonstrators, and also Including Other Valuable Data on 
Roughing and Finishing Cuts; Care and Maintenance of the Gear 
Shapers; Methods of Supporting and Clamping Work; Cutting 
Oils and Cooling Compounds; Gaging and Inspecting 
Gears; Rules for Calculating Elements of 
Geer Teeth; Gear Tables, Etc. 


SECOND EDITION 


PUBLISHED BY 

THE FELLOWS GEAR SHAPER CO. 
SPRINGFIELD, VERMONT 
U. S. A. 



Copyright, 1918 


BV 


The Fellows Gear Shaper Co. 
Springfield, Vermont 
U. S. A. 


‘ < 
c c t 



NOV 


25 


[918 ©Cl. A506722 


| 


INTRODUCTION 


I T should be clearly understood that there is nothing 
difficult about the setting-up and operating of the 
Gear Shaper, and it does not require the atten¬ 
tion of what might be called a “skilled mechanic.” 
In order to become a proficient operator of any machine 
tool it is necessary that the operator make a careful 
study of the various operating members of the machine, in 
order to known when they are functioning properly and 
when they are correctly adjusted. 

J J J 

We employ an experienced staff of engineers, 
experts on the Gear Shaper, and their duties are to 
see that operators of the Gear Shaper are properly 
instructed. It is obvious, however, that these ex¬ 
perts cannot at all times be at hand to answer ques¬ 
tions, and instruct “green” operators, and for this 
reason the Operator’s Handbook has been prepared. 
While all operators do not follow exactly the same 
procedure, there are, nevertheless, certain settings 
that must be made in a certain way. The instruc¬ 
tions as given by our demonstrators are incorporated 
in this Handbook, and we strongly advise that the 
operator constantly refer to it for guidance. 



Fig. 1—The No. 6 Fellows Gear Shaper—Front View 























Fig. 2—Names of Principal Operating Members of the Fellows Gear Shaper 











Fi*?. 3—Group of Spur Gear Shaper Cutters 






CONTENTS 


Chapter I. 

Principles of Operation of the Gear Shaper 


Pages 

1-2 


Chapter II. 

Directions for Setting-up and Operating: 

Order of Setting-up Operations—Example of Gear to Cut— 
Operation i—Selecting and Mounting the Cutter—Opera¬ 
tion 2—Selecting the Change Gears—Operation 3—Select¬ 
ing Work-arbor and Supports—Operation 3-^—Mounting 
and Testing Work-arbor and Work—Operation 3-b— Mount¬ 
ing Work on Arbor and Testing for Concentricity— 
Operation 4—Adjusting Worm in Lower Index Wheel- 
Operation 5—Setting the Change Gears—Operation 5- a — 
Setting the Back Gears—Selecting Cutting Speeds—Opera¬ 
tion 6—Adjusting for Length of Stroke of Ram—Operation 
G-a —Adjusting Ram for Position of Cutter Relative to 
Gear Blank—Operation G-b —Setting Relieving Mechanism 
—Operation 7—Centering Cutter with Gear Blank—Opera¬ 
tion 7 -a —Setting Pitch Dial for Depth of Cut—Operation 8— 
Setting the Timing Mechanism—Operation 8 -a —Setting the 
Double-cut Mechanism—Operation h —Setting Cutter in 
Relation to Blank for Depth of Cut 8 -b —Setting Cutter 
to a Master Gear—Operation 9—Instructions for Oiling 
the Gear Shaper—Operation 10—Starting the Machine 
10 -a-b and c —Operations j and k —Stopping the Machine 
and Removing the Work. 3-34 


Chapter III. 

Roughing and Finishing—Calculating Production: 

Inaccurate Indexing Mechanisms—Advisability of Rough¬ 
ing on one Gear Shaper and Finishing on Another—Neces¬ 
sity for Obtaining Correct Helix Angle—The Helical 
Control Mechanism on the Gear Shaper is Positive—Accu¬ 
rate Gears Should be Roughed and Finished on the Gear 
Shaper—Resetting for Recutting—Calculating Production 
-Summary of Important Points on Roughing and Finish¬ 
ing. 35 “ 4 ° 













VI 


CONTENTS—CONTI NUED 


Chapter IV. 

Care and Maintenance of the Gear Shapers: 


Pages 


Adjusting Worms to Work and Cutter Index Wheels— 
Adjusting Taper Gib in the Cutter-guide on the No. 6 
Gear Shaper—Adjusting Helical Guides on the No. 65 Helical 
Gear Shaper—Adjusting Lower Cutter-spindle Bearing on 
the No. 6 Gear Shaper—Adjusting Lower Cutter-spindle 
Bearing on the No. 65 Helical Gear Shaper—Adjusting 
Taper Gib on the Ram—Adjusting Saddle Gib on Cross¬ 
rail—Adjusting 'Pension on Apron-lever—Adjusting Lead- 
screw Nut—Adjusting Dial-nut—Adjusting Clamping 
Nuts on the Rack-screw—Adjusting Rack-clamp Binder— 
Adjusting Location Block for Apron—Adjusting Work- 
spindle—Adjusting Ring-gib on Upper Index Wheel.41-56 


Chapter V. 

Sharpening Gear Shaper Cutters: 

Sharpening the Spur Gear Shaper Cutter—Sharpening the 
Helical Gear Shaper Cutter—Grade and Grain of Grind¬ 
ing Wheel for Sharpening Spur Gear Shaper Cutter- 
Grade and Grain of Wheel for “dry” Sharpening—Cooling 
Compounds for Cutter Sharpening.57-62 


Chapter VI. 

Methods of Supporting and Clamping Work: 

Faceplate and Work-supports—Cutting on “Pull and 
Push” Strokes—Reduced Travel—Gear Faces Should be 
True with Holes—Cutting Accurate Gears—Work-arbors 
Should be Hardened and Ground—Method of Using a 
Combination of Work-arbor, Faceplate and Work-support 
Methods of Holding Plate Clutch Disks—Methods of 
Holding Automobile Transmission Gears—Holding Shank 
Gears on No. 64 Gear Shaper—Method of Holding an 
Internal Shank Gear—Method of Holding Automobile 
Cluster Gears—Holding Work on Centers—Floating Fix¬ 
tures for Holding Internal Pinions—Fixture for Holding 
Internal Gear Rings—Fixture for Holding Tractor Internal 
Drive Gear—Method of Holding Thin Wall Driving Drum 
for Disk Clutch—Universal Internal Gear Holding Fixture 
—Summary of Important Points on Holding and Clamp¬ 
ing Gear Blanks..63-84 





CONTENTS—CONTI NUE D 


Vll 


Chapter VII. 

Pages 

Cutting Compounds for Gear Cutting: 

Cooling Compounds for Cast Iron—Cutting Oils for Ma¬ 
chinery and Soft Steel—Cutting Oils for Alloy and High- 
carbon Steel—Cooling Compounds for Brass, Bronze and 
Aluminum—Cutting Fibrous Materials.85-87 


Chapter VIII. 

Gaging and Inspecting Gears: 

The Three Essentials of Quiet Running Gears—Concen¬ 
tricity—Correct Center Distances—Properly shaped Tooth 
Curves—Methods of Testing Concentricity of Cut Gears— 
Measuring Center Distances—Conclusion—Summary of Im¬ 
portant Points on Gaging and Inspecting Gears.88-92 


Chapter IX. 


Rules and Formulas: 

Formula for Calculating Change Gears—Example—Form¬ 
ulas for Calculating Production—Example—Rules for Cal¬ 
culating Elements of Gear Teeth—Systems for Calculating 
Elements of Gear Teeth—Forms of Gear Teeth—Names of 
Various Elements of Spur Gear Teeth—Rules for Calculating 
Elements of Standard Involute Gear Teeth—Circular Pitch 
—Diametral Pitch—Conversion of Circular into Diametral 
Pitch—Pitch Diameter—Center Distance—Addendum— 
Clearance—Clearance of Gears Cut on the Gear Shaper— 
Whole Depth of Tooth—Thickness of Tooth—Outside 
Diameter—Number of Teeth—Root Diameter—Involute 
Base Circle Diameter—Pressure Angle—Velocity Ratio— 
Chordal Tooth Thickness and Corresponding Corrected 
Addendum—Pitch Point—Common Tangent.93-109 


Chapter X. 

Rules for Calculating Elements of Internal Gears: 

Interference in Internal Gears—Pitch Diameter—Center 
Distance—Inside Diameter—Involute Base Circle Diameter 
—Internal Clutch Gears—Limits for Size of—Cutting In¬ 
ternal Clutch Gears—Smallest Number of Teeth that Can 
be Cut with the Gear Shaper Cutter.110-116 









Vlll 


CONTENTS—CONTINUED 


Chapter XI. 

Rules and Formulas for Helical Gears: 


Pages 


Advantages and Tooth Action of the Helical Gear—Gear 
Shaper Standard Helical Tooth—Gear Shaper Standard 
Helix Angles—Helical Gear Definitions.117-120 


Chapter XII. 

Tables of Gear Tooth Parts: 

fable VIII-—Gear Tooth Parts, Standard Involute Tooth 
Form—Table IX—Gear Tooth Parts, 20° Stub-tooth Form 
-Table X-—Gear Tooth Parts, Module (Metric) System, 
Standard iqpf 0 Involute Form—Table XI—Gear Tooth 
Parts, Module (Metric) System, 20° Pressure Angle, Stub- 
tooth Form—Table XII—Circular and Diametral Pitch 
Equivalents of Module (Metric) Pitches—Table XIII— 
Hundredths of Millimeters Converted into Inches—Table 
XIV 7 —Decimals of an Inch Converted into Millimeters— 
fable XV—Conversion of Millimeters into Inches—Table 
XVI—Conversion of Fractions of an Inch into Millimeters 
—Table XVII—Conversion of Fractions of an Inch into 
Millimeters, cont’d—Table XVIII—Decimal Equivalents 
of Fractions of an Inch.1-21-132 




CHAPTER I. 


Principles of Operation of the 
Gear Shaper 

' 1 'he Gear Shaper, as its name implies, is a machine for shaping the 
teeth of gears, and it accomplishes this by a method known as the 
generating process. Briefly stated, the principle of operation of the 
Gear Shaper is similar to the action of two gears in mesh. One gear, 
the cutter, is provided with gear teeth which are relieved, as will be 
explained later, to facilitate cutting and to provide for sharpening 
without change of form; and the other, is the blank to be cut. 

The cutter is held on the cutter-spindle retained in the ram that is 
given a reciprocating motion similar to that of an ordinary crank 
shaper. The work is held on an arbor retained in an apron, which 
can be unlocked, when necessary, and swung back clear of the machine 
to remove and replace the work. This apron is also provided with a 
relieving mechanism to withdraw the work from the cutter on the 
return stroke of the latter. Both the work-arbor and the cutter- 
spindle are provided with index wheels, and these are so connected 
by gearing that the cutter and work rotate slowly together similar 
to the action of two gears in mesh, the cutter meanwhile being given a 
reciprocating motion. 

Two independent motions are provided for the feed of the cutter; 
viz., a depth feed, by which the saddle carrying the cutter is fed 
radially into the blank; and a rotary feed, by which the cutter and 
blank are slowly rotated in unison. The rotary feed of the cutter is 
effected by change gears, as will be explained later. Usually, in 
starting to cut a gear, the depth feed is engaged first, and the cutter 
allowed to feed in about three-quarters of the full depth of the tooth, 
before the rotary feed for the cutter is engaged. 

When high-grade gears, however, are being produced in large 
quantities, it is more economical to use one or more Gear Shapers for 
roughing, and another battery of Gear Shapers for finishing. In this 


2 


PRINCIPLES OF OPERATION 


way the same cutter is not called upon to take roughing and finishing 
cuts, and hence, the finishing cutter, which takes only a light cut, will 
stand up much longer and produce better work. The work also has 
a chance to cool off after roughing, and if proper care is taken in re¬ 
mounting for finishing, better results will be obtained than if they 
were roughed and finished at the same setting. I he subject of 
roughing and finishing gears is more fully dealt with in Chapter III. 



Gear Shaper Cutter “Generating” Gear Teeth in a Metal Blank 









CHAPTER II. 


Directions for Setting-up and 
Operating 

The Spur and Helical Gear Shapers operate on the same principle, 
but differ in construction in order particularly to adapt them for the 
work they are intended to perform. The following instructions are, 
therefore, intended to cover all types of Gear Shapers. The pro¬ 
cedure to follow in setting up the Gear Shaper varies to some extent, 
depending upon the shape and character of the work, but there are 
certain fundamental points with reference to the setting-up of the 
machine that should be followed in a certain order, so that the operator 
will not overlook some essential setting or adjustment. The order of 
operations, which are briefly outlined here and more fully described 
later, is that followed by our demonstrators. We, therefore, 
strongly advise operators of the Gear Shaper to follow this procedure 
as closely as possible. 

Order of Setting-up 
Operations 

Operation /:—S elect 
cutter and mount 
on spindle in direc¬ 
tion in which cut is 
to be taken—on 
the ‘‘pull’’ or 
push ’ ’ stroke. 

Caution: See that 
the cutter-spindle, 
washers, etc., are 
perfectly clean. 

Op erati on 2 :—S elect 
change gears and 
mount them on 



Fig. 4—Gear to Cut and Gear Shaper 
Cutter Used 





4 


SETTING-UP AND OPERATING 


studs. Do not mesh gears 
at this time. See Table I. 
(Page 6.) 

Operation j :—Select work-arbor 
or work-supports, depend¬ 
ing on character and shape 
of gear. Clean work-arbor 
and spindle and insert arbor 
in spindle. 

Operation j-a :—Test work-ar¬ 
bor for truth by means of a 
dial test indicator, holding 
indicator so that plunger is 
in line with axis of spindle, 
and rotate by disengaging 
worm from index wheel. 

Maximum eccentricity of 

¥ 

work-arbor, 0.00025 inch. 
(See instructions.) 

Operation j-b :—Assemble work on work-arbor and test for truth, both 
by rotating work on arbor and also by rotating index wheel. 
(See instructions, and also description of Methods of Supporting 
and Clamping Work in Chapter VI.) 

Operation 4 :—Adjust worm in index wheel so that it runs freely 
without backlash. This is important. (See further instruc¬ 
tions under heading—“Adjusting Worm to Index Wheel.”) 

Operation 5:—Adjust the change gears to run freely. (See further 
instructions under heading—“Setting Change Gears.”) 

Operation 5-a :—Set the back gears, in or out, depending on the speed 
of the cutter-ram desired. 

Operation 6 :—Adjust eccentric for length of stroke of ram. 

Operation 6-a :—Adjust ram for position of cutter in relation to gear 
blank—setting varies on spur and helical machines. (See further 
instructions under heading—“Adjusting Ram for Position of 
Cutter,” also chart on Page 21.) 

Operation 6-b :—Set relieving mechanism. Note carefully position of 
crank for direction of cut. (See instructions.) 

Operation y :—Center cutter with gear blank, using setting gage 
supplied with the machine. 















SETTING-UP AND OPERATING 


5 


Operation /-a: —Set pitch dial for depth of cut relative to pitch of gear 
teeth. 

Operation 8 :— Set timing mechanism. 

Operation 8 -a: —Set double-cut mechanism if it is desired to take 
roughing and finishing cuts on the same machine. 

Operation 8 -b: —Set cutter in relation to blank for depth of cut, using 
0.019 inch setting-gage feeler furnished with the machine, or 
master gear. (See instructions.) 

Operation 9:—Oil machine. (See instructions.) 

Operation 10: —Pull machine over by hand to see that the various 
operating members are working correctly. 

Operation 10-a:— Start machine by pulling over shipper lever and 
start feed by raising feed lever. 

Operations 10-b and 10-c: —Stop machine by pulling over shipper 
lever and remove gear blanks. Clean machine and follow pro¬ 
cedure as given under instructions j-a y /-a and 10-a. 

Example of Gear to Cut-In order to make the following descrip¬ 
tion as clear and simple as possible, an example will be taken and 



4 -INCH CUTTER- • ‘PULL’ 1 STROKE 
4 TO 6 PITCH,INC. 


3-INCH CUTTER- 
“PULL” STROKE 
7 TO 1 6 PITCH, INC. 



NOTE WASHER, 
IS TOO Small 


4-INCH CUTTER, 
INCORRECTLY MOUNTED 



4-INCH CUTTER-(THIN WEB) 
“PUSH” STROKE 
4 TO 5 PITCH,INC. 


shank cotter, 
'•POSH-' stroke 

C 


1 

1 







4-INCH CUTTER- 
“PUSH” STROKE 
4 TO 6 PITCH,INC. 


3-inch cutter- 
• ‘PUSH” STROKE 
7 TO 24 PITCH,INC. 


HUB CUTTER. 
“PUSH” STROKE 

H 



Fig. 6—Diagram Illustrating Correct and Incorrect Methods of 

Mounting Cutter on Spindle 







































































































6 


TABLE I. CHANGE GEAR CHART 


Change Gear Combinations 

FOR THE . 

FELLOWS GEAR SHAPER 



CHANGE GEAR ON 


CHANGE GEAR ON 


CHANGE GEAR ON 


CHANGE GEAR ON 

| CHANGE GEAR ON 

Numhw 




Numbrr 















af 

Worn 

Qua4- 

lowtr 


Worm 

Quad- 

Lower 


Worm Quad- 

lower 


Worm 

Quad- 

lower 


Worm 

Quad- 

Lower 

Tntt 

stun 

rant 

Shall 

Tnth 

Shall 

rant 

Shaft 

imh 

Shalt «■ 

Shalt 

Teeth 

Shaft 

raa 

Shalt 

' Teeth 

Shall 

ran 

Shalt 


A 

B 

C 


A 

B 

c 


A 1 B 

c 


A 

B 

c 


1 A 

B 

C 

10 

40 

36 

120 

49 

49 

72 

60 

100 

50 108 

45 

168 

42 

120 

25 

250 

50 

120 

i 20 

11 

44 

36 

120 

50 

50 

72 

60 

102 

68 108 

60 

no 

68 

120 

40 

252 

42 

144 

20 

12 

36 

40 

100 

51 

34 

90 

50 

104 

52 108 

45 

112 

43 

120 

25 

256 

64 

120 

25 

13 

39 

40 

100 

52 

62 

72 

60 

105 

70 108 

60 

174 

58 

108 

30 

258 

43 

144 

20 

14 

42 

40 

100 

54 

54 

72 

60 

108 

54 1 96 

40 

115 

70 

108 

36 

260 

52 

120 

20 

15 

60 

36 

120 

55 

44 

90 

60 

110 

44 108 

36 

176 

44 

120 

25 

261 

58 

108 

20 

16 

48 

40 

100 

56 

56 

72 

60 

111 

37 108 

30 

180 

45 

120 

25 

264 

44 

144 

20 

17 

68 

36 

120 

51 

38 

90 

50 

112 

56 [ 96 

40 

184 

46 

120 

25 

270 

45 

144 

20 

18 

64 

40 

100 

58 

58 

72 

60 

114 

38 108 

30 

185 

37 

120 

20 

272 

68 

120 

25 

19 

72 

38 

120 

60 

48 

90 

60 

115 

46 | 108 

36 

186 

62 

108 

80 

216 

46 

144 

20 

20 

72 

40 

120 

62 

62 

72 

60 

116 

58 96 

40 

188 

47 

120 

25 

279 

62 

108 

20 

21 

72 

42 

120 

63 

42 

90 

50 

117 

39 108 

30 

189 

42 

108 

20 

280 

56 

120 

20 

22 

72 

44 

120 

64 

64 

72 

60 

120 

60 96 

40 

190 

38 

120 

20 

282 

47 

144 

20 

23 

72 

46 

120 

65 

52 

00 

60 

123 

41 108 

30 

192 

48 

120 

25 

288 

48 

144 

20 

24 

72 

48 

120 

66 

66 

72 

60 

124 

62 ! 96 

40 

195 

39 

120 

20 

290 

58 

120 

20 

25 

90 

40 

120 

68 

08 

72 

GO 

125 

50 108 

36 

196 

49 

120 

25 

294 

49 

144 

20 

26 

72 

39 

90 

69 

46 

90 

50 

126 

42 108 

30 

198 

66 

108 

30 

291 

66 

108 

20 

27 

72 

54 

120 

10 

70 

72 

60 

128 

64 96 

40 

200 

50 

120 

25 

300 

50 

144 

20 

28 

72 

56 

120 

12 

48 

108 

60 

129 

43 108 

30 

204 

68 

108 

30 

306 

68 

108 

20 

29 

72 

58 

120 

14 

37 

108 

45 

130 

39 120 

SO 

205 

41 

120 

20 

310 

62 

120 

20 

30 

72 

60 

120 

15 

50 

108 

60 

132 

44 IDS 

30 

207 

46 

108 

20 

312 

52 

144 

20 

31 

72 

62 

120 

16 

38 

108 

45 

135 

45 108 

30 

208 

52 

120 

25 

315 

70 

108 

20 

32 

72 

64 

120 

18 

39 

108 

45 

136 

34 120 

25 

210 

42 

120 

20 

320 

64 

120 

20 

33 

72 

66 

120 

80 

40 

108 

45 

138 

46 108 

30 

215 

4.8 

120 

20 

324 

54 

144 

20 

34 

68 

54 

90 

81 

54 

90 

50 

140 

42 120 

30 

216 

72 

108 

30 

330 

66 

120 

20 

35 

72 

56 

96 

82 

41 

108 

45 | 

141 

47 108 

30 

220 

44 

120 

20 

336 

56 

144 

20 

36 

72 

54 

90 

84 

42 

108 

45 

144 

48 ! 108 

30 

222 

37 

144 

20 

340 

68 

120 

20 

37 

37 

72 

60 

85 

68 

00 

60 

145 

58 108 

36 

224 

56 

120 

25 

348 

58 

144 

20 

38 

38 

72 

60 

88 

43 

108 

45 

141 

49 108 

30 

225 

45 

120 

20 

350 

70 

120 

20 

39 

39 

72 

60 

81 

58 

90 

50 

148 

37 120 

25 

228 

SS 

144 

20 

360 

60 

144 

20 

40 

40 

72 

60 

88 

44 

108 

45 

150 

50 108 

30 

230 

46 

120 

20 

372 

62 

144 

20 

41 

41 

72 

60 

90 

72 

90 

60 

152 

38 120 

25 

232 

58 

120 

25 

384 

64 

144 

20 

42 

42 

72 

60 

92 

46 

108 

45 

153 

34 108 

20 

234 

39 

144 

20 

396 

66 

144 

20 

43 

43 

72 

60 

93 

62 

90 

50 

155 

62 I 108 

36 

235 

47 

120 

20 

405 

90 

108 

20 

44 

44 

72 

60 

94 

47 

108 

45 

156 

39 120 

25 

240 

48 

120 

20 

408 

68 

144 

20 

45 

45 

72 

60 

95 

38 

108 

36 

160 

4S | 120 

30 

243 

54 

108 1 

20 

420 

70 

144 

20 

46 

46 

72 

60 

96 

48 

108 

45 ! 

162 

54 108 

30 

245 

49 

120 

20 

432 

79 

144 

20 

47 

47 

72 

60 

98 

49 

108 

45 

164 

41 120 

25 1 

246 

41 

144 

20 

450 

9(1 

120 

20 

48 

48 

72 

60 

99 

66 

108 

60 

165 

66 108 

36 

248 

62 

120 

25 | 

540 

90 

144 

20 


With cutter having leu than 51 teeth and more than 16 teeth u*e “Pitch Gear” having twice the number of teeth of 
the cutter. 

With cutter having more than 51 teeth use “Pitch GeaH*having the lime number at the cutter, using combination given 
for one half the number of teeth to be cut (Example No. 1) or if the number of teeth to be cut it not divisible by two use 
combination given for that number of teeth, but reduce the size of “A” or “B” by half, or double the size of “C”, (Example 
No. 2) remembering that “A” and “B” can be interchanged without altering the result, (Example No. 3) 

With cutters having less than KTteeth use “Pitch Gear” having four times the number of teeth of the cutter, using com¬ 
bination given for twice the number of teeth to be cut (Example No. 4) 

Example No. 1 

Example No. 2 
or 

Example No. 3 
Example No. 4 


| Gear to be cut--50 teeth, 20 pitch 

A 

B 

C 

“Pitch Gear 

13-inch 20-pitch cutter - 60 teeth 

90 

40 

120 

60 

iGear to be cut—51 teeth, 20 pitch 

A 

B 

C 

“Pitch Gear 

13-inch 20-pitch cutter - 60 teeth 

34 

90 

100 

60 

fGear to be cut—51 teeth, 20 pitch 

A 

B 

c 

"Pitch Gear 

13-inch 20-pitch cutter - 60 teeth 

90 

34 

100 

60 

| Gear to be cut—50 teeth, 7 pitch 

A 

B 

c 

“Pitch Gear’ 

2-inch 7-pitch cutter - 14 teeth 

50 

108 

45 

56 


SPEED AND FEED TABLE 


CAST 

IRON 


Small Step On Cone Small Step On Cone 
200 Strokes Per Minute 200 Strokes Per Minute 

FEED 


STEEL 


Roughing Cut Finishing Cut 

Speed—Strokes per Minute 


Medii 


Coarse 


Speed—Strokes Per Minute 


Small Step On Cone Small Step On Cone 
200 Strokes Per Minute 200 Strokes Per Minute 


It is impossible to give speed and feed tables that can be 
followed blindly as they do not take into consideration the 
important factors of quality, variation of stock, etc. Under 
ordinary conditions the tables given are conservative. If the 
very finest quality of gears for high-speed work is required 
we recommend two cuts. With two cuts, a coarser feed can 
generally be used. Sometimes with a slower speed a coarser 
feed can be used, particularly on hard stock. 

A little experimenting along these lines will increase 
the output of the machine considerably. 


FEED 


Fine 


Medium 


NOTE—Countershaft speed 605 r. p. m. gives 200 strokes using small 
step of cone pulley on machine. 

The number of strokes indicated above is correct for gears of 6 a pitch 
and finer and face widths not exceeding 3 inches. For coarser pitches 
decrease number of strokes 10 to 15 per cent. For wider faces de¬ 
crease number of strokes 15 to 20 per cent. 


g ; 

n 

J^L 




k- 


n 


Diagram of Change Gears 




































































SELECTING AND MOUNTING THE CUTTER 


7 


the various operations described in detail. As an example, we will 
select the gear shown in Fig. 4, which has forty-seven teeth of 6 pitch, 
i-inch face, 7.833 inches pitch diameter, material—cast iron. This 
gear is used in a mechanism where quietness of action is essential; 
hence great care must be exercised in cutting it. 

Operation 1 :— Selecting and Mounting the Cutter —The first step 
is to select the cutter to use, and in this connection, it should be under¬ 
stood at the start that the Gear Shaper cutter, see Fig. 3, is a uni¬ 
versal one. It will cut any gear of its pitch and any number of teeth 
up to the capacity of the machine. The spur Gear Shaper cutter 
as used for the average run of work is made in two sizes, viz., a 4-inch 
pitch diameter cutter for gears of 6 pitch and coarser, and a 3-inch 
pitch diameter cutter for 7 pitch and finer. We, therefore, select a 
cutter of the required pitch, in this case 6, which would mean that a 
4-inch cutter should be selected. We have also decided to finish this 
gear without removing it from the machine, and hence will take rough¬ 
ing and finishing cuts. If large quantities of this gear were required, 
we would use one or more machines for roughing and another battery 
for finishing. An important point to remember is that when possi¬ 
ble, the cutter should 
work on the “pull” 
and not the “push” 
stroke of the ram, 
as shown at A in 
Fig. 6. 

It might be stat¬ 
ed, however, that it 
is sometimes neces¬ 
sary, especially when 
cutting an internal 
gear or a shoulder 
gear in which the 
cutter must run into 
a recess, that the 
cutter be located 
with the face down¬ 
ward and cut on 
the “push” stroke. 

Methods of holding Fig. 7—Selecting and Mounting the Change Gears 






















8 


MOUNTING THE CUTTER 



INDEX-WHEEL 


INDEX-WHEEL GUARO 


- GEAR BLANKS 


ARBOR-NUT 

WORK-ARBOR 


TOP PLATE 


FACEPLATE 


WORK-SPINDLE 


r^i 


GEAR SHAPER 
CUTTER 


CHIP-PAN 


^v//////////////////////,7y,y/ 


s - 

APRON-QUILL 


APRON 


WASHER 


Fig. 8—Section through Work-spindle Showing Reverse Taper 
Work-arhor and Method of Supporting Gear Blanks 


the cutter while cutting in this way are shown at D y E, F y G, and 
//, respectively, Fig. 6. 

Another important point to observe in mounting the cutter on 
the spindle is, first, that the cutter-spindle be prefectly clean, that 
washers of the required diameter be used, and that the top washer 
be ground to the same angle as the cutting angle on the cutter; also 

















































































































































SELECTING THE CHANGE GEARS 


9 



that washers of as large a diameter as possible be used. For example, 
the illustrations shown at A and R , Fig. 6, are correct for 4-inch and 
3-inch cutters, respectively. C, Fig. 6, however, shows a 4-inch 
cutter improperly mounted. The washer in this case is too small 
and does not support the cutter sufficiently to resist the cut. Also, 
it is of a smaller diameter than the recess, and hence exerts an un¬ 
necessary strain on the web of the cutter, tending to crack it even 
before it is in operation. The use of high-speed steel cutters is very 
satisfactory if the simple precaution of mounting them properly on 
the spindle is taken. Caution: Never use a pipe or extension 
wrench upon the regular wrench furnished with the machine. The 
thread on the cutter-spindle is a fine one and the leverage exerted 
by the regular wrench is sufficient to hold the cutter rigidly in place. 

Operation 2 :— Selecting the Change Gears —The next step is to se¬ 
lect the necessary change gears, so that the cutter and work will rotate 
in the correct rela¬ 
tion to each other. 

It has been previ¬ 
ously mentioned 
that the cutter- and 
work-spindles, re¬ 
spectively, are con¬ 
nected by gearing 
and that the func¬ 
tion of the change 
gears is to preserve 
the correct relation 
between the num¬ 
ber of teeth in the 
cutter and the 
number of teeth in 
the gear being cut. 

The correct 
change gears to use 
are obtained from 
the gear chart 
shown in Fig. 7, 
and also in Table I, 
which is supplied 
with e v e r v 


Fig9. —Testing Truth of Work-arbor with Dial 
Test Indicator 
















IO 


SELECTING THE CHANGE GEARS 



Fig. 10—'Testing Concentricity of External Diameter with Bore of Gear Blanks 


machine. The number of teeth in the Gear Shaper cutter varies 
with the pitch, and it is necessary to use a gear in the train of change 
gears having a fixed ratio with the number of teeth in the cutter. 
This gear is called the “pitch gear” and ordinarily, it has twice the 
number of teeth that there is in the cutter. There are exceptions 
to this rule, however, as explained in the Chart, Table I. The “pitch 
gear” is used on the quadrant stud, as shown in the lower portion 
of Table I. “Pitch gears” are furnished with each machine for 
all standard pitches within its capacity. 

As we are setting-up the machine for a 6-pitch gear, using a stand- 













SELECTING WORK-ARBOR AND SUPPORTS 


1 1 

ard 4-inch cutter having 24 teeth, we will select a “pitch gear” having 
48 teeth. The “pitch gear,” it will be noticed, is stamped indicating 
the pitch for which it is to be used and has a hole inch diameter- 
Vs inch larger than the hole in the other change gears. By refer¬ 
ring to Table I, it will be noticed that the change-gear combination 
to cut the required number of teeth in this gear is 47,72, and 60 teeth. 
These should be placed in the order given on the studs A , 5 , and C, 
respectively, as shown in the diagram, Table I. 

At this time the change gears are not brought into mesh, but are 
simply placed on the various studs on which they are to be located. 
The meshing of the change gears is not done until after the work- 
arbor and work have been trued up (see operations j-a and j-£), as it 
is necessary to rotate the index wheel by hand when truing up the 
work-arbor and work. The guard that covers the change gears is also 
left off until later, but should be placed and clamped on the stud after 
the change gears have been properly adjusted. 

Operation j :— Select¬ 
ing Work-arbor and 
Supports —The Gear 
Shaper work-arbor, see 
Fig. 8, differs in one 
noticeable respect from 
other arbors, in that it 
has a reverse taper, and 
is placed in the spindle 
from the lower end. 

As this arbor cannot 
be drawn out of the 
spindle, the work can 
be clamped directly to 
the spindle-nose instead 
of to the arbor itself. 

The tighter the work is 
clamped, the firmer the 
arbor holds. This 
type of arbor makes 
possible the use of face¬ 
plate supporting fix¬ 
tures, supporting gear 
blank s at the rims. Fig. 11—Clamping Gear Blanks on Work-arbor 






12 


SELECTING WORK-ARBOR AND SUPPORTS 





Fig. 12—Testing Truth of Sides with Bore of Gear Blanks 


Owing to this fact it is possible, by using suitable work-holding fix¬ 
tures, to support the work in a very satisfactory manner. Care 
should always be taken to see that the faceplates used have their sur¬ 
faces machined true. 

In the particular gear which we have taken for an example, the 
design is such that supporting plates can be used as shown in Figs. 
8 , io, 11 and 12, respectively. These supports should be as large as 
it is possible to get them, without interfering with the action of the 
cutter in the gear. In other words, they should be only slightly 
smaller than the root diameter of the teeth in the gear. Mounting 
the work in this manner enables the whole unit to be tied together, 
and the work-support can be then brought to bear on the top face of 








MOUNTING AND TESTING WORK 




the top-plate. The design of the gear, of course, governs to a large 
extent the method of mounting to be used; the examples given in 
Chapter VI are, therefore, included to suggest satisfactory mountings 
for different types of gears. The operator of the Gear Shaper should 
study these examples carefully, and in this way obtain a clear under¬ 
standing of the most desirable methods of mounting gear blanks. 

Operation j-a: —Mounting and Testing Work-arbor and Work— 

When setting up the machine for the first time on any particular 
gear, it is advisable to test the work-arbor to see that it runs true. 
The first step is to see that the hole in the work-spindle is perfectly 
clean, and also that the work-arbor is perfectly clean. The arbor 
is then put in place, entering it from beneath the apron as will be 
seen in Fig. 8. The arbor is provided with a reverse taper and can 
be assembled only in this manner. Care should be taken in removing 
the arbor, so as not to burr the thread or bend the arbor. A sharp 
blow with a hammer directly on the top of the arbor, using a piece 
of sheet brass to protect it, is the most satisfactory way to remove it. 

After the arbor has 
been put in place, a dial 
indicator is then at¬ 
tached by a suitable 
holder, preferably to the 
saddle, as shown in Fig. 

9. The saddle is then 
adjusted by means of the 
crank-handle shown in 
Fig. 10, until the indica¬ 
tor spindle is in contact 
with the circumference 
of the arbor. It is best 
to make this test at the 
top end of the arbor so 
that the maximum ec¬ 
centricity will be ob¬ 
tained. 

It is desirable when 
extra good gears are to 
be cut that the work- 
spindle or arbor run ab- 



Fig. 13—Adjusting Worm to Index Wheel 








MOUNTING WORK ON ARBOR 



solutely true. This 
is sometimes, of 
course, impossible 
when holding a large 
number of blanks 
which are not ma¬ 
chined accurately 
and are, therefore, 
liable to spring the 
work-arbor out of its 
true vertical plane: 
but the maximum 
eccentricity in any 
case should never ex¬ 
ceed 0.00025 in. 

Operation 3-b : — 
Mounting Work on 
Arbor and Testing 
for Concentricity— 
The next step is to 
place the gear blanks 
on the work-arbor. 
When it is necessary 
to cut more than one 
gear blank at a time, 
that is, when there 

Fig. 14 — Setting the Change Gears no hub on the gear 

to interfere with this 

method of mounting, supports, as shown in Fig. 8, should be used 
under the gear blanks and on top of them, as was explained in con¬ 
nection with Operation 3. 

Before clamping the gear blanks, they should be tested to see that 
the outside diameters of the gear blanks are concentric with the holes. 
The method of making this test is illustrated in Fig. 10, where it will 
be seen that the clamping nut is released, so that the operator can 
rotate the gear blanks freely on the arbor. The indicator is brought 
in contact with the circumference of the gear blanks, and then the 
latter rotated by hand to determine the amount of eccentricity. The 
permissible tolerance for eccentricity of the outside diameter of gear 
blanks varies to a considerable extent, depending on the use to which 






MOUNTING WORK 


*5 


Table II.—Strokes per Min. of Gear Shaper— 
Countershaft Speed 605 R. P. M. 


Cone on 

Drive Shaft 

Strokes 

per Min. 

Back Gears Out 

Back Gears In 

Small Step on Cone 

200 

90 

Middle Step on Cone 

i $6 

70 

Large Step on Cone 

121 

5 6 


the gears are to be put. It is advisable, however, never to allow gear 
blanks to be eccentric more than 0.005 inch. If it is found that the 
gear blanks are out more than this, trouble will be experienced in 
getting the cutter set to the correct depth by means of the 0.019-inch 
setting gage, see Operation 8 -b. 

Next clamp the work, see Fig. 11, using the work-arbor nut wrench 
supplied for that purpose. The nut should be tightened down suffi¬ 
ciently to eliminate any chances of the gear blanks shifting when 
being cut. It is advisable now to again test the concentricity of the 



Fig. 15—Diagram Showing Position of Back Gears when Driving 
Direct and Through Back Gears 







































i6 


TESTING FOR CONCENTRICITY 



Fig. 16—Position of Yoke Lever when Back Gears are Out 


gear blanks. This second test is necessary in order to determine if 
the faces of the gear blanks are at right angles to the axis of the holes. 
If the faces run out of truth with the holes, then it is certain that 
when they are clamped down face to face, they will spring the arbor 
out of its true vertical plane. 

To make this test, the indicator is again brought in contact with 
the gear blanks and the latter rotated by turning the index wheel by 
hand, as shown in big. 12. If it is found when making this test that 
the gear blanks run out more than they did when they were tested by 
being rotated free on the arbor (see Fig. 10), then it is certain that the 
faces are not true with the holes, and if the difference between the 
two readings on the indicator is greater than the manufacturing 
tolerances permitted for eccentricity of the pitch circle, the gears 
should be removed from the work-arbor and re-faced. This is a very 
important point in connection with the mounting of gear blanks on 
the arbor, as it is impossible to secure accurate work unless the blanks 
are accurately machined. If it is found when making this test that 
the gear blanks do not run out more than when previously tested, 
then we can proceed with the setting-up of the machine. 




ADJUSTING WORM IN INDEX WHEEL 


Operation 4 :— Adjusting Worm in Lower Index Wheel —An impor¬ 
tant point that is many times overlooked by operators of the Gear 
Shaper, is the correct adjustment of the worm in the lower index 
wheel. It is impossible to cut gears accurately with the worm run¬ 
ning loose in the index wheel, so that there is considerable backlash. 
Some operators have the habit of adjusting the worm by means of the 
adjusting screw so that is does not mesh accurately with the teeth in 
the index wheel. This adjusting screw, shown in Fig. 13, is for the 
purpose of preventing any shifting of the worm-stud bracket, and is 
not intended for forcing the worm into contact with the teeth of the in¬ 
dex wheel. In setting the worm to the index wheel, the three clamp¬ 
ing bolts in the worm-stud bracket should be released; then the gear 
which has been clamped on the worm-stud should be caught by one 
hand, as illustrated in Fig. 13, and rotated while the bracket is being 
swung over to bring the worm in contact with the index wheel. It 
is possible at this time to feel any backlash that exists. After this 
setting has been made, the bracket clamping bolts should be tightened 
lightly and at the same time the fit of the worm in the index wheel 
tested by rotating it back and forth. The adjusting screw should 



Fig. 17—Position of Yoke Lever when Back Gears are In 









SETTING THE CHANGE GEARS 


18 



then be screwed in to 
hold the bracket in 
its correct position, 
after which the 
bracket clamping- 
screws should be ful¬ 
ly tightened. 

Operation 5:— 
Setting the Change 
Gears—The correct 
change gears having 
been selected and 
mounted on their re¬ 
spective studs, we 
now bring them into 
mesh and clamp the 
brackets carrying 
them. Many oper¬ 
ators adjust the 
change gears so 
tightly that they give 
a jerky action when 
rotating. The 
change gears should 
be adjusted so that 
they rotate freely 
without excessive 
backlash, and with¬ 
out any jerky action. When making the adjustment for the change 
gears, the crank-handle should be placed on the feed-rod, as shown 
in Fig. 14, and this rotated while the gears are being brought into 
mesh. It is then easy to determine when the gears are running to¬ 
gether correctly. The various clamping bolts should then be tight¬ 
ened to hold the brackets carrying the studs in their correct positions. 
After the change gears are set, and the brackets clamped, the change- 
gear guard is put in place and clamped, so that it does not interfere 
with the free action of the change gears. The function of this change- 
gear guard is to prevent chips from getting in between the teeth of the 
gears and preventing their proper action. It is also provided as a 
safety guard and should be on when the machine is operating. 


Fig. 18—Adjusting for Length of Stroke of Ram 





SETTING THE BACK GEARS 


l 9 


Operation 5-a :— Setting the Back Gears —The setting of the back 
gears is determined by the speed at which the machine is to be oper¬ 
ated. If the material to be cut is very hard, then it is advisable to 
throw in the back gears and run the machine at a slow speed. The 
speed at which the machine is operated is also governed by the length 
of stroke required, and on the average run of work, the machine will 
produce the greatest number of gears when working on a stroke of 
not more than 3 inches. In setting the back gears, they should not 
be brought too tightly into mesh, as they are liable to transmit a 
chattering effect to the cutter-spindle when so adjusted that they do 
not operate freely. 

Owing to the large number of conditions that affect the feed and 
speed of the machine, it is impossible to lay down any hard and fast 
rules that can be blindly followed. What is said here is more in the 



Fig. 19—Setting Cutter in Correct Relation to Gear Blanks 













20 


SELECTING CUTTING SPEEDS 


way of giving the operator some idea of what has been done, so that 
he will have a starting point upon which to work. Experience in 
the operation of the Gear Shaper, as in many other things, is the best 
teacher, and after an operator becomes thoroughly familiar with the 
machine, he will be able to do things which had at first seemed im¬ 
possible. 

Selecting Cutting Speeds 

Provision is made for securing six different speeds—strokes per 
minute of the cutter-ram (see Table II)—the machine being provided 
with a three-step cone, and a back-gear arrangement whereby three 
additional speeds can be obtained. 

Taking the particular example under discussion as a basis upon 
which to work, we are using a 4-inch cutter having 24 teeth, and we 
are cutting grey cast-iron gears having 47 teeth of 6 pitch, 7.833 
inches pitch diameter. These gears, it will be remembered, were 
to be used in a mechanism that required great accuracy, and con¬ 
sequently, we will decide to finish the gear in two cuts—roughing and 
finishing. For the roughing cut, therefore, we will run the machine 
at 156 strokes per minute, and reference to Table II will show that 
the belt should be placed on the middle step on the cone. We will 
use the medium feed, so that the feed belt will be placed on the 
middle cone, see Table I. Using the speed stated, it is necessary to 
run the machine with the back gears out, so that the pinion and gears 
will bear the relation to each other, as shown to the left in Fig. 15. 
Had we desired to run at a slower speed than 121 strokes per minute— 
the slowest speed with the open belt—it would have been necessary 
to put the back gears in, in which case the pinion and gears would 
bear the relative positions given to the right in Fig. 15. 

Reference to Fig. 15 will show what changes are necessary when 
it is desired to run with an open belt or with the back gears in. In 
the position shown to the left of the illustration, pinion F y which is 
solid with the driving cone-shaft, drives gear B through intermediate 
gear G. B is keyed directly to crank-shaft A from which the cutter 
gets its reciprocating motion. 

Had we desired to run with the back gears in, we would have 
driven through internal gear B' y which is solid with B y and thus also 
keyed to A. To do this handle D would be thrown up, as shown to 
the right in Fig. 15. The yoke, to which this handle is connected, 
carries eccentric bushings C in which crank-shaft A is journaled at 


gear shaper 

CUTTER 


SETTINGS FOR CUTTER STROKE 


21 






































































































































































22 


ADJUSTING FOR LENGTH OF STROKE 



Wrench 


nal Driving j 
'"ear 


Crank-Shaft 

ush Stro ke 

Hole ML J Mr 


nnecting-Rod 


Fig. 21—Setting Relieving Mechanism 

each end. The shifting of D thus moves shaft A to a new position, 
separating gears B and G, and bringing F directly into mesh with 
internal driving gear B' on the crank-shaft. 

In order to make these changes it is necessary, as shown in Figs. 16 
and 17, respectively, to release the two clamping bolts (on which the 
wrenches are shown), and then by gripping the handle, as shown, 
raising the yoke to throw the back gears in, and lowering it to throw 
them out. This yoke, as previously mentioned, carries an eccentric 
bushing which shifts the position of the internal driving gear, moving 
it into or out of contact with the pinion F y shown in Fig. 15. 

Operation 6 .— Adjusting for Length of Stroke of Ram— Like any 
other crank shaper, it is necessary to adjust the cutter-slide for length 
of stroke. This adjustment is made as shown in Fig. 18. The nut 
on the crank-pin is first released, and then the crank-handle placed 
on the adjusting screw. This is rotated until the pointer lines up 
with the graduation corresponding to the width of face of the 
gear, or group of gears, held on the work-arbor. Provision is made 






ADJUSTING RAM FOR POSITION OF CUTTER aj 

so that an additional travel for clearance is provided for. In this 
case, the three gears make a total of 3 inches, so that we will set the 
indicating pointer at 3 inches. The machine then automatically 
takes care of the additional 3%-inch, giving ^ inch clearance for the 
cutter at the top and bottom of the gear blanks. As will be explained 
later, this ^-inch over-travel is divided between the top and bottom 
surfaces of the gear blanks in different amounts. Note:—When 
using the “push” stroke the counterbalance spring shown in Fig. 51 
should be placed on the counterbalance screw and the lock-nuts 
tightened to give the proper tension. This spring is used to take 
care of any backlash in the pinion and rack on the cutter-ram. 

The remarks made here apply only to the setting of the spur 
cutter. On the helical cutter it is necessary to provide for additional 
clearance, owing to the fact that this cutter has not a plain face, but 
has the individual teeth ground at an angle at right angles to the 
helix angle of the cutter. Consequently, more excess travel is 
necessary for the helical than for the spur cutter. 

Operation 6-a :—Adjusting Ram for Position of Cutter Relative to 
Gear Blank— The next step is to set the cutter in the correct relation 
to the gear blanks, as shown in Fig. 19. Before making the setting, 
it is necessary to have the apron seating properly, and the lock- 



Fig. 22—Centering Tooth of Gear Shaper Cutter in Line with Axis of Gear 













24 


ADJUSTING]RAM FOR POSITION OF CUTTER 



ing plungers hold¬ 
ing the apron in 
place. The belt 
should be pulled 
around by hand so 
that the cutter- 
slide is at the lower 
end of the stroke. 
The operator now 
places the crank- 
handle on the rack 
adj usting-screw, 
this having previ¬ 
ously been released 

j 

by loosening the 
clamping nut rack- 
screw clamp, shown 
Fig. 25. The 


Fig. 23—Setting Pitch Dial for Depth of Cut 


operator then ro¬ 
tates this screw and 
brings the cutter in 
the correct relation 
to the bottom of 
the gear blanks, if 
cutting on the 
“pull” stroke, and 
at the top of the gear blanks, if cutting on the “push” stroke. The 
correct amount of clearance between the top face of the cutter and 
the lower face of the gear blanks is inch, and this is provided for 
by means of a ^--inch feeler gage supplied with the machine. 

The different settings for “pull” and “push” strokes both on the 
spur and helical Gear Shapers are illustrated in Fig. 20. A shows 
the position of the spur cutter in its two positions—at the bottom and 
top of the stroke, when working on the “pull” stroke—whereas B 
shows the relative positions of the spur cutter when working on the 
“push” stroke. On shoulder or cluster gears, as well as internal 
gears, the setting of the pointer on the crank should be made slightly 
less than the number indicating the face width of the gear, so that the 
total excess travel of ^5 inch is not obtained. This is essential, 
especially when the cutter is of coarse pitch, and the space or clear- 










ADJUSTING RAM FOR POSITION OF CUTTER 


2 5 



ance into which the cutter runs is not greater than Y or ^ inch. The 
cutter should be set so that it just breaks through in order to prevent 
the packing up of chips, and the liability of chipping the teeth of the 
cutter. This setting is much more important than the one shown at 
A, and the operator should use great care in seeing that it is properly 
handled. The setting should also be tested each time a new blank 
is put in place. 

C shows the setting of the helical cutter in relation to the gear 
blanks when working on the “pull” stroke. Here, it will be noticed, 
that at the bottom of the stroke the top face of the teeth should be 
set Y2 inch below the lower face of the gear blanks, whereas at the 
top of the stroke, the lower cutting point or rear face of the cutter 
teeth should set ^2 inch above the top face of the gear blanks. The 
amount of excess travel necessary to give this clearance varies with 
the pitch of the cutter and its helix angle, and it is necessary, of 
course, in each individual case to set the pointer so that sufficient 
excess travel is 
obtained at the top 
and bottom of the 
stroke. 

In setting the 
Helical Gear Shap¬ 
er cutter to work on 
the “push” stroke 
for cutting a cluster 
or interna] helical 
gear, practically 
the same remarks 
apply as in the case 
with the diagram 
illustrated at B , ex¬ 
cept that at the 
bottom point of the 
stroke, the clear¬ 
ance should not ex¬ 
ceed Yj to inch. 

In other words, the 
cutter should be 
made so that it sim¬ 
ply breaks through 


Fig. 24—Setting the Timing Mechanism—Adjusting 
Stop Pins for Single Cut 




26 


SETTING RELIEVING MECHANISM 



the blank, in order, 
as has been previous¬ 
ly stated, to prevent 
the packing up of the 
chips and the liabili¬ 
ty of chipping the 
cutter. A good 
point to note here is 
that a greater clear¬ 
ance or recess for the 
cutter to run into is 
necessary when using 
a helical cutter than 
when using a spur 
cutter. The actual 
clearance necessary 
is dependent on the 
pitch and the helix 
angle of the cutter 
and should never be 

Fig. 25 —Setting the Timing Mechanism ^ ess than }4 inch. 

and Bell Ringer Operation 6-b :— 

Setting Relieving Mechanism —As we have decided in this case to 
operate the machine on the “pull” stroke, it is necessary now to see 
that the relieving mechanism, which withdraws the work from the 
cutter on the return stroke of the latter, is properly set. This setting 
is made at the rear of the machine by removing the connecting-rod 
stud from the “push” stroke hole (if it has been previously set in this 
position), and inserting it in the “pull” stroke hole. The stud is 
removed by the wrench illustrated in Fig. 21, the internal gear disk 
rotated and the stud inserted in the “pull” stroke hole. At the same 
time care should be taken to see that the apron is closed so that the 
plungers will not come down on top of the rolls. 

Operation p :— Centering Cutter with Gear Blank —When using 
the 0.019-inch thickness feeler for setting the cutter for depth of cut, 
it is necessary that one tooth of the Gear Shaper cutter be located on 
the axis or center line of the work-spindle in order that a true reading 
may be obtained. To do this the setting gage provided with the 
machine is held up against the saddle in the position shown in Fig. 22, 
and the feed-rod turned by the crank-handle, as illustrated, until the 






SETTING PITCH DIAL 


27 


center of one tooth of the cutter is in line with the front edge of the 
setting gage. When a master gear is used for setting to depth, this 
operation is not necessary. Unless it is definitely known that the 
gear blanks are accurately machined, the setting gage should not be 
used. When gears of one type are being made in quantities, a 
master gear is preferable. 

Operation J-a :— Setting Pitch Dial for Depth of Cut —Setting the 
cutter for depth of cut is simple. The graduations for depth on the 
dial give the setting for each pitch or module. To make the setting, 
withdraw locking pin, as shown in Fig. 23, then place crank-handle 
on dial pinion-shaft, and rotate to left; this turns the pitch dial to 
the right, and it is advisable to bring the pitch line desired past the 
zero point on the feed bracket, and then back again, so as to take up 
all backlash in the screws and gears. For cutting stub-tooth gears, 
say 6/8 pitch; set pitch dial for 8 pitch and select change gears for 
number of teeth. Note: When the locking pin is withdrawn it 
should be rotated, so that it is held out by the locking step on the 
bushing. 

Operation 8 :— Setting the Timing Mechanism —The timing 
mechanism of the 
Gear Shaper is con¬ 
trolled by means of 
a cam, located inside 
of the dial gear, 
which is operated 
automatically by 
means of ratchets 
and pawls. This 
cam has two depres¬ 
sions and when the 
timing mechanism is 
set for t a k i n g a 
double cut, it only 
makes one-half a rev¬ 
olution to one full 
revolution of the gear 
blank. In other 
words, it makes one- 
half revolution, when 

the rotary feed is Fig. 26—Setting the Double-cut Mechanism 







28 


SETTING DOUBLE-CUT MECHANISM 



Fig. 27—Setting Cutter in Relation to Gear Blank 
for Depth of Cut, Using 0.019-Inch Feeler 


automatically thrown 

out, and the depth 

feed in. When the 

cutter has been fed 

in to the full depth, 

the depth feed is again 

automatically dis- 

✓ 

engaged and the ro¬ 
tary feed is thrown 
in. Upon one com¬ 
plete revolution of the 
cam, the rotary feed 
is thrown out and a 
bell rung to notify 
the operator. 

The position of the 
stop pins A and B y 
Fig. 24, determines if 
a gear is to be finished 
in one or in two cuts. 
If the gear blank is 
to be finished in two 
cuts, these stop pins 
are pushed in as far 
as they will go; where¬ 


as if they are withdrawn to the full distance, the gear will be fin¬ 
ished in one cut. Stop pin B is withdrawn or forced in by adjust¬ 
ing the knurled nut that is located between the head of the screw 
and the dial clamp-pin sleeve-nut. 

To set the timing mechanism, both stop pins A and B , as illus¬ 
trated in Fig. 24, are withdrawn. The crank-handle is then placed 
on the timing shaft, as illustrated in Fig. 25, and this is rotated to 
the left until the feed-trip bracket is thrown towards the machine. 
This setting can be determined by noting the position of the bell 
ringer, which drops into place in front of the driving studs on the 
cone-cover. The starting lever is now thrown up, as far as it will 
go, this action rotating the cam to the starting position. 

Operation 8-b :— Setting Double-cut Mechanism —In the example 
under discussion, we have decided to finish the gear blank in two 
cuts, so that it is necessary to set the double-cut mechanism. This 







SETTING CUTTER FOR DEPTH OF CUT 


2 9 



setting is handled in the manner shown in Fig. 26. The wrench is 
placed on the dial binding-nut, the latter released, and then the 
nut moved over until the zero mark on the flange reaches the grad¬ 
uation equalling the amount that it is desired to leave for the second 
cut. Say in this case that we are allowing 0.010 inch on the pitch 
diameter, then the zero mark on the nut is set opposite 10. When 
this setting has been made, the binding-nut is again tightened. In 
setting the double-cut mechanism care should be taken to see that the 
pitch setting has not been disturbed, and if it so happens that it has, 
the setting should be re-made on the order previously given. 

Operation 8-c :—Setting Cutter in Relation to Blank for Depth of 
Cut —The machine is 
now ready to set the 
cutter in the correct 
relation to the gear 
blank for depth of cut. 

There are two meth¬ 
ods of accomplishing 
this. One is by means 
of the 0.019-inch feel¬ 
er, as indicated in Fig. 

27; and the other, by 
means of a master 
gear, as illustrated in 
Fig. 28. The method 
shown in Fig. 27 is 
not recommended 
w h e n it has been 
found that the out¬ 
side diameter of the 
gear blanks is not 
concentric with the 
hole, or when the 
blanks are over or 
undersize. If the 
blanks, however, are 
correctly sized and 
concentric, this 
method can be used. 

The crank-handle is 


Fig. 28—Setting Cutter for Depth of Cut, 
Using Master Gear 






SETTING CUTTER TO A MASTER GEAR 


Fig. 29—Front View of Gear Shaper. Showing Bearings that Require Oiling 

placed on the saddle pinion-shaft, and the saddle adjusted over 
until the 0.019-inch feeler will just pass between one tooth of the 
cutter (the cutter, of course, having been previously centered, see 
Operation 7), with the axis of the work-arbor. In making this 
setting, care should be taken to see that the feeler is properly held so 
that it will not be cramped and a false reading obtained. 

Setting Cutter to a Master Gear 

If it is found in testing the gear blanks for concentricity that they 
vary considerably; also that they vary considerably in diameter, 
then the method shown in Fig. 28 should be used, especially when a 
master gear is at hand. This setting consists in placing the master 
gear on the work-arbor, but not clamping it, as illustrated, and then 












INSTRUCTIONS FOR OILING 3I 

bringing the cutter into mesh with it by operating the crank-handle 
on the saddle adjusting screw. The gear and cutter are both left 
unclamped, so that they can be rotated together to get a close setting. 

When the “master gear” method is used, the pitch dial is set at 
zero, in which case the locking pin, Fig. 23, would be in as far as it 
will go. Then after the cutter is properly adjusted to the master gear, 
the cutter is clamped tightly on the spindle, and the dial set for pitch, 
as described in connection with Operation 7 -a. The stop pins are 
also adjusted in if two cuts are to be taken. The adjustment of these 
pins automatically sets the double-cut and timing mechanisms. 
Operation 9 :— Instructions for Oiling the Gear Shaper —The Gear 



Fig. 30—Rear View of Gear Shaper, Showing Bearings that Require Oiling 











STARTING THE MACHINE 


3 2 


Shaper is now com¬ 
pletely set up, and be¬ 
fore starting it in opera¬ 
tion, it is necessary to 
thoroughly oil all the 
working parts. Care¬ 
ful attention given to 
the oiling of the Gear 
Shaper, of course, will 
greatly increase its life, 
and some of the work¬ 
ing parts, especially the 
apron seat, as shown 
in Fig. 29, should be 
oiled at least twice a 
day, and when cutting 
large gears, every time 
the apron is opened. 
The necessity for this 
will be appreciated 
when it is stated that 
the apron moves back 
and forth on the seat once for every stroke of the machine. It, 
therefore, is a bearing surface that is greatly used and requires 
lubrication. Another member that requires lubrication is the 
cutter-slide. On the later type of machine an oil wiper arrange¬ 
ment is inserted in the head, and it is necessary to fill this container 
only once or twice a week, depending upon the number of hours 
that the machine is in continuous operation. On the old type of 
machine, the cutter-slide bearing should be oiled not less than twice 
a day. All the other oil cups indicating bearing surfaces on the 
machine are illustrated in Figs. 29, 30 and 31, respectively. These 
cups should be kept filled and cleaned out occasionally to make sure 
that the oil is getting to the bearing surfaces. 

Operations 10 and 10-a :— Starting the Machine —Before pulling 
over the shipper lever to start the machine, it should be turned over 
by hand, as illustrated in Fig. 32, principally to see that all the 
operating mechanisms are working properly. One point that should 
receive careful attention is the relieving mechanism. The operator 
should go behind the machine, pull over the belt in the direction 



Fig. 31—End View of Gear Shaper, Showing 
Oil Cups that Require Filling 












STARTING THE MACHINE 


33 



indicated by the arrow, and make sure that the apron is closed and 
that the plungers are not coming down on top of the rolls on the 
relieving arm; also noting that the plunger stud is in the correct hole, 
for “pull” or “push” stroke. The setting of the cutter in relation to 
the gear blanks should also be tested, making sure that the cutter 
travels far enough on each side of the blank to clear, and that the set¬ 
ting, previously 
made for position ol 
the cutter relative 
to the gear blank, 
was correctly made. 

By pulling over 
the belt by hand a 
couple of times, it 
can be determined 
whether the various 
operating mechan¬ 
isms are function¬ 
ing properly. The 
next step is to pull 
over the shipper 
lever, starting the 
driving mechanism 
of the machine. 

The operator then 
lifts up the starting 
lever, as illustrated 
in Fig. 33, which 
engages the depth 
feed and the ma¬ 
chine automatically 
starts up. When 
using the double¬ 
cut mechanism, the 
sequence of opera¬ 
tions is as follows: 

The cutter first 
feeds into roughing 
depth. The oper¬ 
ator then releases 


Fig. 32—Operator Pulling over the Machine by 
Hand to see that the Various Members 
are Working Properly 






34 


STOPPING THE MACHINE 


the bell-ringer pin so 
that it contacts with 
the square driving 
pins on the cone-cover 
(see Fig. 33), this en¬ 
gaging the rotary feed. 
The gear blank now 
makes one complete 
revolution with the 
cutter working at 
roughing depth. The 
rotary feed is now 
disengaged automati¬ 
cally, and the cutter 
feeds into full depth. 
Upon the completion 
of the second revolu¬ 
tion, the feed is auto¬ 
matically thrown out 
and a bell rung to 
notify the operator. 
Operations 1 o-b and 
10-c :—Stopping the Machine and Removing the Work —As soon as 
the bell has been rung, the operator immediately withdraws the bell¬ 
ringer pin from out of contact with the square pins on the cone-cover; 
then lifts up the starting lever, pulls over the shipper lever and stops 
the operation of the machine. He then determines whether the 
plungers are out of engagement with the rolls, and it so, the lever is 
placed in the apron hinge and the latter released. The apron can 
then be swung open so that the work can be easily removed. The 
operator now resets the dial to pitch, this automatically withdrawing 
the cutter from the work. The arbor nut is then released and the 
gear blanks removed from the arbor. Another set of gear blanks 
is put on, care being taken to see that the work-holding fixtures, 
arbor, etc., are perfectly clean. The work is then clamped, and it 
is best to pull the belt by hand and note if the cutter is clearing the 
top and bottom faces of the gear blank. This precaution should 
always be taken when cutting helical internal or shoulder gears. 
The shipper lever is now pulled over and the machine started as 
described in connection with Operation \o-a. 



Fig. 33—Operator Lifting-up Starting Lever to 
Start Machine in Operation 




CHAPTER III. 


Roughing and Finishing—Calculating Production 


It is the practice, especially in the production of gears for automobile 
transmissions, to take two cuts—roughing and finishing. In some 
cases the roughing operation is handled on another type of machine, 
and the finishing cut taken on the Gear Shaper, the belief being that 
the roughing operation is unimportant, and, consequently can be 
accomplished on any type of machine where metal can be removed 
expeditiously. That this is a fallacy can be very clearly proved, and 
the operator should be instructed to pay just as much attention to 
the roughing operation as he does to the finishing. A gear that is not 
properly roughed is difficult to finish correctly. There are many 
reasons for this, but only the more important ones will be mentioned 
here. 

Inaccurate Indexing Mechanisms 



In roughing out a spur gear on a machine in which the indexing 
mechanism is not correct, it is evident that the teeth in the gear will 
not be evenly spaced leaving an unequal amount of stock to be removed 
from the sides of the teeth. This evidently exerts an excessive strain 
on the machine used for finishing, with the result that unless the 
machine is very carefully adjusted and kept in first-class repair, it 
will not, in most cases, be able to entirely remove the errors in one 
cut. Two finishing cuts are then necessary when high-grade gears 
are desired. The necessity for three cuts can be obviated by taking 
the necessary care when roughing. 


Advisability of Roughing on One Gear Shaper 
and Finishing on Another 

When spur gears are being produced in large quantities it is general¬ 
ly much more satisfactory to do the roughing on one battery of Gear 
Shapers and the finishing on another group of Gear Shapers. It is 
also good practice to use the older machines for roughing and the 
newer machines for finishing. This does not mean, of course, that 



36 


ROUGHING AND FINISHING 


the old machines should not be kept in good repair and properly 
adjusted. It is also advisable to use a roughing Gear Shaper cutter 
for roughing spur gears. This cutter is made with a slightly thinner 
tooth on the pitch line than the finishing cutter, and the top lace is 
ground to a cutting angle of io degrees instead of 5 degrees, as is the 
case with the finishing cutter. Of course, the standard finishing 
cutter can be used for roughing, but it does not work as fast as the 
roughing cutter, due to the fact that it leaves more material to be 
removed by the points of the teeth of the cutter used for finishing. 

Necessity for Obtaining Correct Helix Angle 

Another point that deserves attention, and which applies more 
particularly to helical gears, is the necessity of obtaining the correct 
helix angle when roughing gear blanks. When helical gears are 
roughed out on a machine in which the helix angle is controlled by 
the setting of an index head and a combination of change gears, it is 
not always possible to get the exact helix angle desired. The form 
of tooth produced also varies from that produced by the Helical Gear 
Shaper cutter. If the helix angle is not made right in the roughing 
operation, the finishing cutter will be called upon to start in with a 
fight cut and finish up with a heavy one, or vice versa . When this 
is the case it is difficult to obtain a helical gear having the desired 
helix angle with one finishing cut. The same remarks would also 
apply to the depth of tooth made in the roughing operation, as was 
described in connection with the roughing of spur gears. If the 
roughing cutter is of such shape that the tooth is not made to full 
depth, then it leaves too much material for the ends of the teeth of the 
finishing cutter to remove in the finishing operation. Consequently, 
the finishing cutter does not stand up as long and does not produce 
as smooth a finish as when it has less strenuous work to do. 

The Helical Control Mechanism on the Gear Shaper is Positive 

In the Helical Gear Shaper, the helix angle is controlled by positive 
helical guides. Hence, it is impossible for the operator to make an 
incorrect setting. Further, the teeth of the Helical Gear Shaper 
cutter are ground after hardening, so that each tooth does its share 
of the work, and also produces teeth that are of the correct involute 
form. It is, therefore, evident that if a helical gear is roughed on the 
Gear Shaper in which duplication of guides and cutters is a certainty 


CUTTING ACCURATE GEARS 37 

the finishing Gear Shaper cutter will be working under ideal condi¬ 
tions. From the standpoint of production, as well as accuracy, the 
Gear Shaper when used for both roughing and finishing is superior to 
any other known method for the production of both spur and helical 
gears. 

Accurate Gears Should be Roughed and Finished 
on the Gear Shaper 

We strongly recommend the roughing and finishing of gears on 
the Gear Shaper. Manufacturers, who have adopted this practice, 
find that in the end it is the best-paying policy. They have less 
trouble in cutting accurate gears and less trouble with the up-keep 
of the machine. The Gear Shaper is then not called upon to perform 



Fig. 34—Operator Resetting Gear Blank for Recutting 






















38 


RESETTING FOR RECUTTING 


the function of a correction machine for other operations handled 
improperly on other machines, and consequently, is working to its 
best advantage. If the gears are roughed on the Gear Shaper, then 
only one finishing cut is necessary to cut a high-grade gear. If the 
gears are roughed on any other machine, then in many cases it 
becomes necessary to take two finishing cuts on the Gear Shaper, so 
that in the long run roughing and finishing on the Gear Shaper is the 
best policy to follow. 

Resetting for Recutting 

When roughing gears on one Gear Shaper and finishing on another, 
it is necessary to reset the gear blanks with reference to the cutter and 
the pitch dial for the second cut. This is accomplished in the manner 
illustrated in Fig. 34. The first step is to mount the work-arbor in 
the work-spindle and test for truth with the dial indicator, see 
Operation 3-a. If the machine is being set-up for the first time on 
this particular gear, then it is necessary to perform Operations 1 to 
6-b inclusive, before setting the cutter to the roughly cut blanks. 
After these operations have been satisfactorily completed, the oper¬ 
ator cranks the dial pinion-shaft until the locking pin drops in. Then 
with the gear blanks mounted on the work-arbor, but not clamped, he 
C»yiks the saddle adjusting-screw, as shown in Fig. 34, until the 
F/tter is brought into correct mesh with the teeth of the gear; after 
which the gear blanks are securely clamped. Before clamping the 
gears, the teeth in the roughly cut blanks should be lined up. 

The locking pin is then withdrawn and the cutter backed away 
from the work, by placing the crank-handle on the dial pinion-shaft. 
The cutter should be backed away an amount slightly exceeding the 
amount that it is desired to remove in the finishing cut. The next 
step is to again place the crank-handle on the saddle adjusting-screw. 
The micrometer on the lead screw is first set, counting from the zero 
point, to the number of thousandths that are to be removed in the 
finishing cut, and the cutter is then fed in by this amount by operating 
the saddle adjusting-screw. The setting is now complete, and the 
next step is to pull over the shipper lever and start the machine, as 
described under Operations 9 to xo-c, inclusive. 

Calculating Production 

There are two methods of determining the time required to cut a 
certain gear on the Gear Shaper. The first and most satisfactory 
one, is to actually cut a batch of gears and note the time required to 


CALCULATING PRODUCTION 


39 


complete them. The second method is to calculate the time required 
for the cutter to feed in to full depth, and the work to make one com¬ 
plete revolution. If the gear is to be completed in two cuts, then 
it is necessary to determine the time required to make two complete 
revolutions. When the product is determined by calculation, it is 
necessary, of course, to assume a certain speed and feed, and also the 
time required to mount and remove the gear blanks, set and start 
the machine. These last factors are governed by the size and shape 
of the gear to be cut, and the type of work-holding fixture used. 

The approximate speed and feed at which the Gear Shaper should 
be operated when cutting gears of various pitches is given in Table 
I, and as an example of a calculation to find the production, we will 
say that it is necessary to cut an 8-pitch gear having a pitch diameter 
of 6 inches, 48 teeth. The cutter used would be 3 inches pitch 
diameter, 24 teeth. Assuming that the material is cast iron, we will 
assume a speed of 156 strokes per minute as being satisfactory, 
using the medium feed. 

An approximate but simple rule for calculating the production is as 
follows: Multiply the following factors 1400 for fine feed; 1000 for 
medium feed and 750 for coarse feed; depending on the feed selected, 
by the number of teeth in the gear, and divide the product obtained 
by the product of the number of teeth in the cutter times the stroke^ 
that the machine makes per minute. Using the values for number oL ' 
teeth in the gear and cutter, and the number of strokes given in the 
preceding paragraph, we find that the time to cut this gear taking 

1000X 48 

one cut is equal to-=12.82 minutes, or approximately 12 

24 X156 

minutes and 49 seconds. If it is desired to take two cuts, the result 
given is simply multiplied by 2. 

This approximate formula does not take into consideration the 
time required to remove and replace the work or set the machine. 
For further information on this subject, the operator is referred to 
Chapter IX. 



4 o 


ROUGHING AND FINISHING GEARS 


Summary of Important Points on Roughing and 
Finishing Gears 

The question of roughing and finishing gears is of vital importance 
to the manufacturer who wants both accuracy and production. 
There are several important points to observe in this connection, and 
the vital ones are summarized in the following paragraphs. 

Operators of the Gear Shaper should understand that the roughing 
operation should be handled with the same care as the finishing 
operation. Unless the roughing operation is properly handled, 
difficulty will be experienced in accurately finishing the gear. 

If a gear is roughed out on a machine in which the index wheel is 
not accurate, the teeth of the gear will be unevenly spaced with 
the result that the gear cannot always be accurately finished with one 
finishing cut. 

When great accuracy is required, it is preferable to rough out the 
gear blanks on one Gear Shaper and finish on another. The finishing 
machine should be carefully adjusted and care taken in resetting for 
recutting. 

The Fellows Helical Gear Shaper differs from all other gear-cutting 
machines used for cutting helical gears, in that the Helical Gear 
Shaper Cutter is at all times under perfect control. It -is neither 
fiexibly mounted nor flexibly operated. 

Helical gears which are required to be accurate, should be both 
roughed and finished on the Helical Gear Shaper. 

Operators who desire to become proficient on the Gear Shaper 
should study very carefully, the points outlined in Chapters II and 
III. 


CHAPTER IV. 


Care and Maintenance of the Gear Shapers 

In addition to that of keeping the Gear Shaper well oiled, it is also 
advisable, especially on machines used for finishing, to see that all 
excessive play between the moving members is taken up. Metals 
which are subjected to a rubbing action or friction, wear, and the 
Gear Shaper is no exception to this rule. Great pains has, therefore, 



Adjusting Screw 


Binding Blits 


Wrench 


Worm-Box i 




Screw Driver 






. 




Fig. 35—Adjusting Worm in Cutter Index Wheel for Wear 

been taken in all cases to provide for wear of the moving parts. The 
operator should pay particular attention to those functions or mem¬ 
bers of the machine where a close fit is essential to the continued 
accuracy of the machine. In the following, a description is given 
of the methods used in adjusting the various members of the Gear 
Shaper, these adjustments being given in the order of their importance 
relative to the continued accuracy and efficiency of the Gear Shaper. 




42 


ADJUSTING GIB IN CUTTER-GUIDE 



Jjib 

—Gib Adjusting 


Lockin 

Nut 


Wrench 


, U ' 

; i} 


Screw Driver 


Index Wheel 




Fig. 36—Adjustment of Taper Gib in Cutter-guide 
on No. 6 Gear Shaper 


The method used 
in adjusting the low¬ 
er worm to the work- 
spindle indexing 
wheel has been pre¬ 
viously described in 
connection with 
Operation 4. Owing 
to the fact that the 
lower worm is dis¬ 
connected from the 
index wheel to true 
the arbor and work, 
a more frequent ad¬ 
justment is necessary 
than is the case with 
the upper worm. It 
is advisable, how¬ 
ever, to test the mesh 
of the upper worm in 
the index wheel, to 
see that there is no 
excessive play. The 


method of making this adjustment is shown in Fig- 35. The worm- 
bracket clamping screws that hold the worm-bracket to its seat on 
the saddle are first released, then the worm-bracket adjusting-screw 
is moved in or out to obtain the proper fit of the worm. 

After the screw has been adjusted, the crank-handle is placed 
on the feed-rod, as illustrated in Fig. 22, and the latter rotated to 
determine if the fit or mesh of the worm in the index wheel is correct. 
Another test, which is made after the clamping bolts are tightened, 
is to place the wrench on the cutter-spindle; then hold one hand on 
the index wheel and at the same time move the wrench to see if there 
is any backlash. Care should be taken to see that all backlash be¬ 
tween the upper index wheel and worm is removed. In order to cut 
accurate gears it is necessary that the cutter be kept in proper step 
with the work. Excessive backlash is, therefore, to be avoided. 


Adjusting Worms to 
Work- and Cutter- 
index Wheels 












ADJUSTING GIB IN CUTTER-GUIDE 43 

Adjusting Taper Gib in the Cutter-guide 
on the No. 6 Gear Shaper 

In the No. 6 Gear Shaper, a straight guide for the cutter-spindle 
is used. One part of this guide is fastened to the cutter-spindle, and 
the other is attached to the member carrying the upper index wheel. 
The guide attached to the cutter-spindle is reciprocated back and 
forth past the guide held in the index wheel, and in order to provide 
for wear an adjustable taper gib is supplied, as shown in Fig. 36. In 
order that the fit of these two guides be just right, it is necessary 
occasionally to re-adjust the taper gib. To do this, the nut and 
counterbalance spring are removed from the counterbalance spring 
stud, when the hood covering the upper member of the index-wheel 
casing can be removed. Then by means of a wrench the lock-nut 



Fig. 37—Adjusting Helical Guides on No. 65 Helical Gear Shaper 



44 


ADJUSTING HELICAL GUIDES 



Fig. 38—Two Views of the Helical Guide Assembly—Removed 

from the Machine 

is releaseci and the adjusting screw, as illustrated, turned to the right, 
forcing the taper gib down between the faces of the two guides. The 
gib is adjusted down until the guides will move past each other with 
the necessary freedom, but without any play. To test the fit of the 
guides, the driving belt should be pulled by hand, and if the guide 
goes down with a hesitating action, it is a sure indication that the 
gib is adjusted too tightly. The gib should be adjusted to a point 
where it will not overcome the weight of the ram. After the proper 
adjustment has been secured, the lock-nut is again tightened and the 
hood replaced as before. If the guides are adjusted too tightly, 
chatter marks will sometimes show up prominently on the gear teeth. 

Adjusting Helical Guides on the No. 65 1 lelical Gear Shaper 

To adjust the helical guides satisfactorily on the No. 65 Helical 
Gear Shaper, it is necessary to remove the guide casing and the 
helical guide from the ram. To remove the casing from the index 
wheel, it is necessary to unscrew the two clamping bolts. The 
flanged nut on the top of the cutter-spindle is then backed off, and in 
doing this, the jack, which is clamped to the top of the guide, thus 
loosens the guide from the cutter-spindle. Then the case is free to 
be lifted out of the index-wheel case. As is shown in Fig. 39, this 
helical-guide mechanism comprises three principal parts: one, the 
gib and shoe, which is split into two pieces, is held inside the second 
member or casing; the third is a one-piece guide, which is attached to 






ADJUSTING LOWER CUTTER-SPINDLE BEARING 


45 


the cutter-spindle. The method of adjusting this guide is clearly 
shown in Fig. 37. The assembled unit is removed from the machine, 
as previously mentioned, and is caught between the jaws of a vise, as 
illustrated. A stick of wood is then forced into the cutter-spindle 
guide, so that it can be moved back and forth freely. The locking 
screw is then released sufficiently to allow the adjustable member of 
the guide to be moved. The adjustment for wear is then taken up 
by means of an adjusting screw on which a wrench is placed, as 
shown in Fig. 37. This should be turned to the left to withdraw the 
adjustable member for taking-up for wear. This adjustment is made 
so that the guide attached to the cutter-spindle will move freely past 
the other guide without any binding action, and also without any 
play. When the desired adjustment has been obtained all of the 
locking and binding screws are tightened. The member is then 
placed back into the machine in the manner in which it was removed. 

Adjusting Lower Cutter-spindle Bearing on 
No. 6 Gear Shaper 

The cutter-spindle is retained in bearings, the upper one of which 
is non-adjustable, while the lower one against which most of the 
thrust of the cut is taken, is adjustable. This adjustment is made by 
three clamping screws, as shown in Fig. 40. The lower bearing is 
split and the lower end of the ram is so made that it can be adjusted 
in to tighten the fit of the bearing on the spindle. When it is found 
that the spindle is a loose fit in the bearing, this adjustment should 
be made. To do this, the clamping screws are tightened. The 
change gears are then disconnected, and by means of the crank-handle 
which should be located on the feed-rod, the spindle is rotated. 



Fig. 39—The Helical Guide Mechanism Dismantled 








46 


ADJUSTING LOWER CUTTER-SPINDLE BEARING 





1 * % mi mini * imifimi 


--—---- 


Adjusting Screws 
Screw Driv 


Cutter-Spindle 




Fig. 40—Adjusting Lower Cutter-spindle Bearing on No. 6 Gear Shaper 

The screws are tightened until the spindle starts to bind; then re¬ 
leased about one-eighth of a turn. A loose lower spindle-bearing 
is sometimes the cause for chatter marks being produced on the 
teeth of gears. 


Adjusting Lower Cutter-spindle Bearing on 
No. 65 Helical Gear Shaper 

The adjustment of the lower cutter-spindle bearing on the No. 65 
Helical Gear Shaper requires a little more attention than that of the 
No. 6 machine for the reason that the cutter-spindle in addition to 
being slowly rotated, also receives a twisting motion, which tends to 
wear the bearing more rapidly. In order to provide for this the 
cutter-spindle bearing is designed a little differently than that of the 
No. 6. The method of making the adjustment on the No. 65 Helical 
Gear Shaper is shown in Fig. 41. The three adjusting screws which 
are provided with lock nuts, fit in a taper slot, as shown in the upper 
sectional view, and are used for expanding the bronze bushing. The 
other three clamping screws are used for drawing the bearing tightly 







ADJUSTING TAPER GIB ON RAM 


47 


BRONZE SPINDLE 
BEARING 



onto the cutter-spindle. To make the adjustment the nuts on the 
adjusting screws are released, and then the adjusting screws turned 
to the right. The three clamping screws are tightened until the 
spindle starts to bind. Then the clamping screws are backed off 
one-eighth of a turn and the nuts on the adjusting screws tightened 
to a bearing. The fit is determined by turning the feed-rod. 

Adjusting Taper Gib on the Ram 

The ram, which is reciprocated back and forth in the saddle by 
means of the crank mechanism of the machine, is also provided 
with an adjustable gib. 

In order that there may 
be no excessive play be¬ 
tween the ram and its 
bearing in the saddle, 
this gib should be ad¬ 
justed. To do this the 
two clamping screws, as 
shown in Fig. 42, are re¬ 
leased, and then the 
adjusting screw turned 
to the right, forcing the 
gib up into the saddle 
and removing the play 
between it and the ram. 

The clamping screws are 
then tightened after ad¬ 
justing the gib, in order 
to prevent the gib from 
being drawn up into the 
saddle and breaking off 
the lower end below the 
adjusting slot. To 
make the test the ma¬ 
chine is pulled over by 
hand to determine the 
fit, as mentioned in con¬ 
nection with the adjust¬ 
ment of the gib in the 

upper index-wheel bear- Fig. ^—Adjusting Lower Cutter-spindle 

ing of the No.6 machine. Bearing on No. 65 Helical Gear Shaper 


-—-<2 










(D 


7*---h 


SPINDLE-BEA 


CLAMPING 

screws' 



> 


LOCKNUT v 

ki 



©, 


O 


, SPINDL 

a’d 1 





I 

E-BEARI 

LISTING 

fREWS 

I 
























































































































4 8 


ADJUSTING LEAD-SCREW NUT 



In order to provide 
for wear between the 
bearing in the saddle 
and its seat on the 
cross-rail, an adjust¬ 
able gib is provided, 
as shown in Fig. 43. 
To make this adjust¬ 
ment the clamping nut 
is released and the 
adjusting screw 
turned to the right 
until by the feel of 
this screw, it has been 
found that the gib is 
brought to a bearing. 
The clamping nut is 
again tightened, and 
the crank-handle 
placed on the saddle 

Fig. 42 —Adjusting Taper Gib on Ram pinion-shaft, when 

the fit of the saddle 

can be determined by cranking it back and forth on the cross-rail. 


Adjusting Saddle Gib 
on Cross-rail 


Adjusting Lead-screw Nut 

The saddle is moved back and forth on the cross-rail by means of 
the lead screw, and in order to remove any backlash between the 
lead-screw nut and the lead screw an adjusting nut is provided. To 
make this adjustment, the headless screw is released and the adjust¬ 
ing nut tightened, see Fig. 44. The headless-screw is then tightened, 
and the crank-handle placed on the saddle pinion-shaft. This is 
then rotated back and forth to determine if there is any backlash 
between the lead-screw nut and the lead screw. Backlash at this 
point will make readings on the micrometer collar inaccurate. 

Adjusting Dial Nut 

The pitch dial is held on the right-hand end of the lead screw by 
means of a triple thread, and up against a bearing in the housing by 







ADJUSTING TENSION ON APRON-LEVER 49 

the dial adjusting-nut. In order to prevent any backlash between 
the thread in the pitch-dial and the lead screw, an adjusting nut is 
provided, as shown in Fig. 45. To remove the backlash, the headless- 
screw, shown, is released and the nut tightened in the same manner as 
described in connection with the adjusting of the lead-screw adjust¬ 
ing-nut. To test for backlash, the crank-handle is placed on 
the dial pinion-shaft, and the latter rotated to determine the fit. 
When the adjustment has been made the headless-screw is again 
tightened. 

Adjusting Tension on Apron-lever 



When the apron operating-plungers are being assembled they 
are set in the correct position and pinned to the plunger-head. 
The roll-carrier on the 
apron-lever is adjusted, 
so that the lever is sprung 
T§- inch by means of the 
locking plunger. This 
serves to hold the apron 
tightly in place in its seat 
when the cut is being 
taken. 

This setting is properly 
made before the machine 
leaves the factory, and 
rarely does it require re- 
adjusting. If adjust¬ 
ment, on account of 
wear, however, is found 
to be necessary, the Gear 
Shaper is pulled over by 
hand until the roll is on 
the flat part of the lock¬ 
ing plunger. A scratch 
mark is now drawn a- 
cross the roll-carrier and 
roll-carrier support, as 
indicated in Fig. 47. 

The connecting rod is 

now disconnected from Fig. 43 — Adjusting Saddle-gib on Cross-rail 





5° 


ADJUSTING TENSION ON APRON-LEVER 



Fig. 44—Adjusting Lead-screw Nut 

the plunger-head, and the plungers removed. Now, pull the apron- 
lever back by hand as far as it will go, and if it is found that the mark 
on the roll-carrier is less or more than yg inch away from the mark 
on the roll-carrier support, then the roll-carrier must be adjusted 
until this distance is obtained. To accomplish this, the binding 
screws on the roll-carrier are released, and the nuts on the adjusting 
screw are turned until the mark on the roll-carrier support is yg inch 
closer to the machine than that on the roll-carrier. 

When the adjustment has been made, the binding screws are again 
tightened, and the adjusting nuts brought up tightly on each side of 
the apron-lever. The plungers are now put back in place, and con¬ 
nected up to the connecting-rod head. Caution: Whenever an 
adjustment is made on the roll-carrier, the eccentric stud in the apron- 
lever, on which the relieving roll is held, must also be adjusted to 
correspond. 

As has been previously explained in connection with the operation 
of the Gear Shaper, two apron operating-plungers are provided—one 
for locking the apron, and the other, for opening or relieving it, 






ADJUSTING TENSION ON APRON-LEVER 


5 1 


to remove the work 
from the cutter on the 
return stroke of the 
latter. It is essential 
that the relieving roll 
be in contact with the 
Hat face of the plun¬ 
ger, in order that the 
work be relieved from 
the cutter the correct 
amount, to prevent 
rubbing. When 
either the roll or the 
flat face on the plun¬ 
ger become worn, it is 
necessary to adjust 
the eccentric stud 
carrying the roll. To 
do this, the clamping 
screw (not shown in 
Fig. 46, but indicat- 



Fig. 45—Adjusting Dial-nut 



Fig. 46—Adjusting Eccentric Backing-off 
Roll Stud on Apron-lever 


ed by means of the 
small wrench that 
is placed on it), is 
released and then 
the eccentric stud 
turned until the roll 
contacts with the 
flat face of t h e 
plunger. When 
this has been ac¬ 
complished, the 
binding screw is 
again tightened. 
This adjustment 
should be carefully 
made, to obtain the 
correct relation be- 
tween the two 
plungers. 











52 


ADJUSTING NUTS ON RACK-SCREW 




Adjusting Clamping Nuts 
on the Rack-screw 


The reciprocating 
motion of the cutter- 
slide is transmitted 
from the crank 
through a rack carried 
on the crank-arm, two 
pinions on the rock 
shaft, and a rack on 
the cutter-ram. In 
order to set the cutter 
vertically in relation 
to the gear blanks, a 
rack-screw is provided 
for changing the posi¬ 
tion of the rack in 
relation to the pinion 
on the rock-shaft. It 
is essential that there 
be no excessive end 
motion between this 
Fig. 47—Adjusting Tension on Apron-lever rack-screw and the 

rack held on it, and in 
order to provide for 
wear, two clamping 
nuts, as illustrated in 
Fig. 49, are provided. 

To adjust the nuts, 
the headless binding 
screws are released, 
and by means of a 
spanner wrench, the 
nuts tightened. To 
determine the fit, the 
clamping screw on the 
rack-screw, illustrated 
in Fig. 25, is released, 
then by placing the 

crank-handle on the Fig. 48 — Adjusting Location Block for Apron 











ADJUSTING APRON LOCATION BLOCK 


53 



Rack-Guard 


rack-screw, the latter can be rotated to determine il there is any play. 
After the adjustment has been made, the binding screws are again 
tightened, also the clamping screw on the crank-arm. 


Adjusting Rack-clamp Binder 

The rack-clamp which performs the function of transmitting 
motion from the crankshaft to the cutter-ram is so provided that it 
can be clamped to the rack-screw, alter the latter has been adjusted 
to set the cutter in the correct relation to the work. This rack- 
clamp, as shown in Fig. 50, is split at the forward end and is provided 
with a binder and two stop-screws. The function of the stop-screws 
is to prevent break¬ 
age of the rack- 
clamp, and care 
should be taken to 
see that these are 
set correctly. The 
proper method ol ad¬ 
justing these is as 
follows: First, the 
stop-screws are re¬ 
leased, then the rack- 
clamp binder is care¬ 
fully tightened until 
it is found by placing 
the crankhandle on 
the rack-screw that 
it will not t u r n . 

The stop-screws are 
now adjusted in as 
tight as they will go. 

Further adjustment 
of these stop-screws 
is unnecessary until 
the rack-screw or 
thread on the rack- 
clamp wear. In no 
case should the 
binder stop-screws 
be w i t h d r a w n to 


Crank-Handle 


m 


k Spanner Wrench 


Lock Nuts 


Fig. 49—Adjusting Clamp Nuts on Rack-screw 










54 


ADJUSTING LOCATION BLOCK FOR APRON 



Fig. 50—Adjusting Rack-clamp Binder 

such an extent that the full clamping effect of the hinder will come 
on the rack-clamp. 

Adjusting Location Block for Apron 

In order to guide the apron properly into its seat in the frame of 
the machine, a location block, as shown in Fig. 48, is provided. This 
block does not locate the apron except in so far as to guide it to its 
seat in the cabinet. Owing to the small amount of friction that 
takes place, the wear is very slight, so that adjustment is seldom 
necessary. 

If it is found that wear has taken place, the correct position of the 
block can be obtained by smearing the seat with red lead, and then 
the block adjusted so that when the apron contacts with its bearing 
it will bear evenly on the seat. To do this, the machine is operated 
under power, until it has made several strokes. Then the apron is 
opened and the seat inspected. While the machine is running, care 
should be taken, to observe if the apron in closing moves in a straight 
line. If upon close observation, it is found that the apron in closing 
travels in a straight line, and also takes its seat properly; then the 








ADJUSTING WORK-SPINDLE 


55 



SpannerWrencf^ 


Adjusting Nut 


block is correctly adjusted. On the other hand, if the apron moves 
out when closing, the block is in too far, and if it bears only on the 
outer portion of the seat, the block is out too far. 

To make the adjustment, the clamping screw is released, and the 
adjusting screw turned to bring the block to the desired position and 
then the binding screws securely tightened. 

Adjusting Work-spindle 

The work-spindle fits in a tapered seat in the apron-quill, and is held 
in place at the bottom by means of a locking nut, as shown in Fig. 51. 
Continuous rotation of the work-spindle wears the thrust washer 
that is located between the top surface of the lower index wheel 
and the lower bearing surface on the cabinet. To make the adjust¬ 
ment, the worm is disconnected from the index wheel, the binding 
screw backed off from the clamping nut, and then the index wheel 
rotated by hand at the same time as the nut is being tightened by 
means of the spanner wrench. The nut is tightened until the washer 
is brought to a light bearing. The clamping screw is then tightened, 


Lower Index Wheel 


Fig. 51—Adjusting Work-spindle 




>6 


ADJUSTING RING-GIB ON UPPER INDEX WHEEL 


and the worm brought into mesh with the index wheel and adjusted, 
as mentioned in connection with the adjusting of the worm in the 
lower index wheel in Operation 4. 

Adjusting Ring-gib on Upper Index Wheel 


The upper or cutter index wheel, 



Fig. 52—Adjusting Ring-gib on Upper 
Index Wheel 


as shown in Fig. 52, is held down 
on its seat in the saddle by 
means of an adjusting ring- 
gib. When wear takes place 
between the index wheel and 
the upper bearing surface on 
the saddle, the gib should 
be adjusted down to secure 
the necessary fit. This is ac¬ 
complished by means of tour 
adjusting screws of the head¬ 
less type. T hese are tightened 
until a bearing is obtained 
between their points and the 
countersunk spots in the ring- 
gib. Ot course, it is evident 
that the index wheel should 
be allowed to be driven freely 
by the worm without binding. 
In order to make the test 
alter adjusting this gib, the 
crank-handle can be placed 
on the feed-rod and the latter 
rotated. T his adjustment on 
the No. 65 Helical Gear Shaper 
should be looked after more 
frequently than on the No. 6 
Machine, for the reason that 
a greater thrust is exerted 
at this point. T he adjusting 
screws on the ring-gib should 
be tightened until a bearing 
can be felt by turning the 
feed-rod by means of the crank- 
handle. 








































































































CHAPTER V. 


Sharpening Gear Shaper Cutters 

The importance of keeping the Gear Shaper cutter sharp cannot 
he too strongly emphasized. A dull Gear Shaper cutter cannot he 
expected to produce a smooth finish any more than can any other dull 
cutter. Furthermore, a dull cutter consumes much more power, and 
does not remove the metal as fast as a sharp cutter. It is such a 
simple proposition to sharpen the Gear Shaper cutter that there is 
no plausible excuse for using a dull one. A properly adjusted Gear 
Shaper and a sharp Gear Shaper cutter is the one sure and easy way of 
securing accurately cut gears. 

Sharpening the Spur Gear Shaper Cutter 

The sharpening of the Gear Shaper cutter, see Fig. 53, is a simple 
proposition—a plain job of face grinding. No indexing is necessary 
on the spur cutter. There are two common methods of sharpening 



Fig. 53—Spur Gear Shaper Cutter 

the Gear Shaper cutter; one is to use a universal grinding machine as 
shown in Fig. 54, holding the cutter by means of an expansion pin 
chuck and centering it to run true, and then setting the head off to an 
angle of 5 degrees. The sharpening of the cutter is then a simple 
matter of traversing the cutter past the face of the grinding wheel. 

Another method, and a preferable one where a rotary surface 
grinder is to he had, is shown in Fig. 55. In this case, the cutter is 









58 


SHARPENING HELICAL GEAR SHAPER CUTTER 


centered to run dead true on the magnetic chuck by means of a close- 
fitting brass plug, and care should be taken to see that the top face is 
ground true with the back face. The work-table is set off from the 
vertical position to an angle of 5 degrees, and the cutter sharpened 
by traversing the grinding wheel back and forth across the face of the 
cutter. 

Sharpening the Helical Gear Shaper Cutter 

The Helical Gear Shaper cutter, see Fig. 56, requires a little more 
careful attention in sharpening than does the spur cutter. It is 
sharpened in a manner somewhat similar to that of a milling cutter, 



Fig. 54—Sharpening Spur Cutter on Universal Grinder 


but is a much simpler proposition. As is shown in Fig. 58, two angu¬ 
lar settings are required to sharpen the Helical Gear Shaper cutter. 
One angular position is governed by and is the same as the helix angle 
of the cutter tooth. The other is the top rake, and is set at 5 degrees, 
the same as the spur cutter. The preferable way to sharpen the 
Helical Gear Shaper cutter is to use a tool and cutter grinder, as 
shown in Fig. 57, and on this, use the special attachment that is sold 
for this work by the Fellows Gear Shaper Company. 






SHARPENING HELICAL GEAR SHAPER CUTTER 59 

Reference to Fig. 58 will show that the cutter is held on an extended 
arm of the attachment that can be swivelled to the desired angle 
corresponding with the helix angle of the cutter teeth—making the 
face of the tooth at right angles to the helix angle. The arm, in 
addition, is located permanently at an angle of 5 degrees with the top 
face of the cutter-grinder table. The indexing mechanism consists 
simply of a spring stop, the front end of which is made to fit in the 
space between the teeth. Before setting the spring stop, however, the 
cutter should be centered by means of the centering gage (shown 



Fig. 55—Sharpening Spur Gear Shaper Cutter on Rotary Surface Grinder 


detached from the fixture, in Fig. 57), provided for that purpose; and 
the tooth used for centering the cutter is the first tooth on which the 
grinding is done. The index plunger swivel plate (see Fig. 58) is 
then adjusted so that the indexing plunger stop will locate properly 
in the space between the cutter teeth. The sharpening is done by 
traversing the cutter back and forth beneath the grinding wheel. The 
wheel should be kept with a true face, and for this purpose, a diamond 
truing device, which is held on the table of the grinding machine, is 
used. Light cuts should be taken in order to avoid burning the 
cutter, as it is impossible to use a coolant. 





6 o 


GRADE AND GRAIN OF GRINDING WHEELS 



Fig. 56—Right and Left-hand Helical Gear 
Shaper Cutters 


Grade and Grain of Grinding 
Wheel for Sharpening Spur 
Gear Shaper Cutter 

Spur Gear Shaper cut¬ 
ters which are made from 
high-speed steel require 
considerable car 3 in 
grinding in order to pre¬ 
vent checking of the cut¬ 
ter face, caused by un¬ 
equal heating and cool¬ 
ing. For this reason, the 
spur cutter should always 
be ground “wet” and a 
copious supply of cutting 
compound or w a t e r 


furnished. On the 
universal grinding 
machine, as shown 
in Fig. 54, this is a 
little more difficult 
of accomplishment 
than on the vertical 
rotary surface 
grinder, see Fig. 55. 

The grinding 
wheel to use is 
governed by several 
conditions, viz., 
depth of cut, speed 
of wheel, and cut¬ 
ting compound 
used. For our own 
work, we find that 
an alundum wheel, 
grain 46, grade J, 
operated at 4500 
surface feet per min¬ 
ute, gives the best 
results. This wheel 



Fig. 57—Sharpening Helical Gear Shaper Cutter on 
Tool Grinder Equipped with Special Helical 
Cutter Sharpening Fixture 







GRADE AND GRAIN OF GRINDING WHEELS 


61 


is io inches in diameter, %-inch face. The cutter is rotated at a 
speed of 120 feed per minute. The depth of cut recommended should 
not exceed 0.0015 inch per traverse of the wheel over the work, and 
the traverse feed should not exceed 20 inches per minute. The last 
three or four traverses should be made without any up feed to the 
work-table, so as to get a smooth finish. The cutter while being 
ground should be completely submerged in a cutting compound or 
water. 

Grade and Grain of Grinding Wheel for “Dry” Sharpening 

In sharpening the Helical Gear Shaper cutter more trouble would 
be secured in furnishing a copious supply of cooling compound, and 
for this reason, the helical cutter is always ground “dry.” The 
grinding wheel which has been found to give the best results is an 
alundum wheel, grain 46, grade J, 4 inches in diameter, } 4 -'mch face. 
'This is operated at a surface speed of 4300 feet per minute. The 
traversing of the cutter under the wheel is done by hand, and the up 


INDEXING PLUNGER SWIVEL PLATE 

INDEXING PLUNGER STOP 

LOCATING PLUNGER STOP 



Fig. 58—Diagram Illustrating Angles at which Helical Cutter 

is Held when Sharpening 




















































62 


GRADE AND GRAIN OF GRINDING WHEELS 


feed per traverse should not exceed o.ooi inch per traverse. It is 
advisable to take a large number of light cuts rather than fewer 
heavy cuts, for the reason that if the cut is too heavy the face of the 
cutter teeth will become checked. 

The cutter should be kept as cool as possible, and it is preferable 
to cut slowly rather than check the face of the cutter. For finishing, 
the cutter is indexed around twice without any feed, so as to get a 
fine smooth finish on the cutter-teeth faces. 

Cooling Compounds for Cutter Sharpening 

The cooling compound for wet grinding is a question that there is 
considerable difference of opinion on. Water is about as good a 
coolant as can be obtained, but it has the disadvantage of rusting 
the moving members of the machine. A cooling compound which 
has been used with good results is soda water. This comprises one 
pint of sal soda to io quarts of water. The solution is mixed cold 
and applied in the usual manner. 


CHAPTER VI. 

Methods of Supporting and Clamping Work 

The methods used in holding and clamping work 
on the Gear Shaper differ considerably from those 
applied to any other type of gear-cutting machine. 
In order to fully explain the difference, it will be 
necessary to take up briefly some of the principal 
features of the Gear Shaper and explain how they 
differ from those of other machines. In the Gear 
Shaper there are two points that are different, viz., 
the design of the work-arbor and the comparatively 
short stroke of the ram. The work-arbor, as shown 
in Fig. 59, has a reverse taper and can be assembled 
in the work-spindle (see Fig. 60) only from the 
lower end. Inasmuch as this work-arbor cannot be 
drawn up out of the work-spindle, the work can be 
clamped directly to the spindle-nose instead of to 
the arbor itself. It is, therefore, evident that the 
Taper Work- tighter the work is clamped, the firmer the arbor is 
arbor held j n the spindle. 

Faceplate and Work-supports 

This inverted type of work-arbor makes possible the use of a face¬ 
plate for supporting the gear blank at its rim. In this way, tipping 
of the gear blank is avoided, and the blank can be supported right up 
to the point where the cutter is working on it. In addition, the work 
support can be placed directly over the cut (see Fig. 60), taking most 
of the thrust directly against the main frame of the machine, and 
relieving the arbor of all thrusts, enabling it to perform its proper 






6 4 


FACEPLATE AND WORK-SUPPORTS 


function—that of simply locating the work true with the line ol travel 
of the cutter. Many arrangements of faceplates are possible. I he 
arrangement of the faceplate, of course, is governed entirely by the 
shape and character of the work. When cutting an internal gear 



LOWER SURFACE 
OF FACEPLATE" 
OR WORK 


WORK- 

ARBOR 


APRON 


CHANGE 

GEARS 


CUTTER-RAM 


CUTTER-SPINDLE — 
CUTTER 


WORK-SUPPORT 


ROLL-SUPPORT 


GL 1 I T\ TOP PLATE 



ron -rprri 

UJ. - &£J- 

\ , /[ 




WORK-SPINDLE 

APRON-QUILL— 


"ZZZZZL 


1 

V. 1 

H— 

1 

1 

) 




SPECIAL WORK-SUPPORT 
FOR INTERNAL GEARS 

' GEAR BLANKS 

FACEPLATE ROLL-SUPPORT, 


LOWER INDEX-WHEEL 


Fig. 60—Section Through Work-spindle Showing Construction 


that is larger in diameter than the nose ol the work-spindle, the gear 
or fixture is supported by the outer support held in the apron, which 
is made in two types, as shown in Fig. 60. One type is held directly 
in the apron and adjusted by lock washers; whereas the other type 
is held in a special bracket, attached to the apron, as shown in the 

































































































































































“PULL” ANI) “PUSH” STROKE 


6 5 


detail view. A few examples of applications of faceplates for support¬ 
ing the work will be given in the following. 

Cutting on the “Puli’’ and “Push” Strokes 

l he Gear Shaper can be operated just as effectively either on the 
push or pull stroke. Owing, however, to the rigid design of the 
work-arbor, and the practice of clamping the entire unit directly to 
the nose of the work-spindle, it is preferable, when possible, to use the 
“pull” stroke. The cutting strains in this way are distributed to 
the main frame of the machine and are thus absorbed by the massive¬ 
ness of the construction. In cutting cluster, shoulder or stepped 
gears, it is impossible in most cases to use the “pull” stroke, so that 
the “push” stroke is necessary. When slender gear blanks, there¬ 
fore, are being cut on the “push” stroke, it is advisable in all cases 
to use a good rigid faceplate or fixture supporting the gear blanks at 
the rim. When cutting internal gears which are larger in diameter 
than the spindle-nose, the faceplate or fixture is made to rest on the 
support held in the apron. "Phis prevents any distortion of the blank 
and holds it rigidly against the thrust of the cut. 

Reduced Travel 

Another distinctive feature of the Gear Shaper is the reduced 
travel of the cutter. Owing to the fact that in milling gears on a 
milling machine, time is saved by cutting a long string of gears at one 
setting, the idea has become prevalent that this is a desirable method; 
that it is not will be clearly understood when its disadvantages are 
explained. On the Gear Shaper there is no advantage in grouping 
the gear blanks. The reason for this is that the Gear Shaper uses a 
planing cutter and operates on the reciprocating principle, traveling 
a distance only slightly greater than the width of face of the blank; 
and, therefore, there is no advantage of a long travel of the cutter. 
Phis is not true, of course, of the milling cutter, which must travel a 
certain distance before it is buried into the work, so that there is 
considerable excess travel necessary in order to finish the width of 
face. The amount of travel necessary is governed by the diameter 
of the cutter and the depth to which it penetrates into the work. 
This is the reason why on the milling machine, gear blanks are grouped 
in order to save on the idle time required to bury the cutter in the 
work. Idle disadvantage of this method is that with gear blanks in 


66 


CUTTING ACCURATE GEARS 


which the rims are not true with the holes, the errors are multipled 
by the number of blanks held on the arbor at one time. 

Gear Faces Should be True with Holes 

A considerable amount of the trouble experienced in cutting gears 
is due to the fact that the rims of the blanks are not true with the 
holes; that is, they have not been faced square with the hole. It 
is, therefore, obvious that by reducing the number of blanks that are 
clamped together at one time, the effect of these errors is thereby 
reduced. On the Gear Shaper, therefore, when accurate work is 
required, grouping of gear blanks is not a preferable method of 
securing the desired results. Under ordinary conditions the best 
results will be obtained by limiting the travel of the cutter to between 
2 and 3 inches. 

Cutting Accurate Gears 

One of the fundamental requirements of gear cutting is that in 
order to have gears run satisfactorily, they must be mounted to run 
on precisely the same axis as that on which they are cut. In high¬ 
speed gearing, an eccentricity of 0.002 to 0.003 inch will make noisy 
gearing, and it is only by careful attention to all the various details 
that this error can be kept within the necessary fine limits. 

As has been previously mentioned in connection with the operation 
of the Gear Shaper—see Operation a —the work-arbor should be 
tested in its position in the work-spindle with an indicator each time 
it is placed in the machine. The maximum amount of eccentricity, 
which in any case should be allowed, is 0.00025 inch, but it is preferable 
to have the work-arbor run “dead” true. Generally the arbor is 
perfectly straight, but a small piece of dust or dirt either on the 
arbor or in the hole of the work-spindle causes the arbor to run out a 
slight amount. By removing the arbor and turning it around a 
fraction of a turn, the error can sometimes be eliminated. 

Work-arbors Should be 1 Iardened and Ground 

Under no conditions should a soft work-arbor be used. Arbors 
should either be made from machinery steel pack-hardened and 
ground, or from tool-steel hardened and ground. A good pack- 
hardened machinery steel arbor is satisfactory. If bushings are 
used, care should be taken to see that they are true, and it is preferable 
to grind them. They need not be hardened unless there is a large 


WORK-SUPPORT, ARBOR AND FACEPLATE 


6 7 


number of gears to cut. All washers or faceplates used for supporting 
the gear blanks, should be kept true and faced off evenly either on a 
grinding machine or on a lathe to insure that the faces are square 
with the hole. Gear blanks which have been found to be inaccurately 
machined should be corrected before the teeth are cut. This is es¬ 
pecially necessary if it is found that the faces of the rims are not true 
with the holes. 

Experience has shown that money spent for first-class equipment 
tor holding gear blanks, and for keeping them to a high standard, is 



Fig. 61— A —Method of Holding Cast-iron Gear Blanks 
B —Method of Holding Automobile Engine Timer Gears 


money well spent. If the work is handled under the right conditions, 
elaborate inspection of gears after cutting is not necessary. Given a 
cutter—similar to the Gear Shaper cutter—that produces the correct 
tooth form, the principal gear trouble is one of eccentricity. Machine 
the blanks correctly and this trouble disappears. 







































































































































































68 


WORK-SUPPORT, ARBOR AND FACEPLATE 


Method of Using a Combination of Work-arbor, 

Faceplate and Work-support 

The illustrations A and B , Fig. 61, show two methods of using a 
combination of the work-arbor, faceplate and work-support. A 
shows a common application of the faceplate system to the holding 
of armed gears. If ten or more of these blanks were clamped to¬ 
gether, a total of the errors in rim thickness of each gear might result 
in a sprung work-arbor. Inasmuch as grouping of gear blanks on 
the Gear Shaper, however, does not increase production, we can limit 
the number of gears held at one time to three or four, when the face 
width is one inch. Reference to this illustration will show that the 



WORK-SUPPORT 


TOP 

WASHER 


CUTTER- 

SPINDLE 


^FIXTURE 


PLATE 
DISK I 


LOWER CUTTER 

WASHER 

WORK-SPINDLE"'" 


WORK- 

ARBOR 


APRON-QUILL 


CUTTER-SPINDLE 


CHIP 

HOLES 


Fig. 62— A —Method of Holding External Plate-clutch Disks 
B —Method of Holding Internal Plate-clutch Disks 


gear blanks are supported at the rim by the faceplate, and then a top 
plate, which is of the same diameter as the faceplate, is used for 
clamping the gear blanks at the rim. The work-support then rests 
on the surface of the top plate, so that the entire members are very 
rigidly supported. This makes an ideal combination. 

The illustration B in Fig. 61 shows a method of holding automobile 
timer gears. In this case, in order to increase the stiffness, the fixture 
is provided with an extended bushing made integral with the face¬ 
plate. The bushing part of the fixture is used for locating the gear 












































































































HOLDING PLATE-CLUTCH DISKS 69 

blanks centrally. It will also be noticed that the top plate is used. 
I his is advisable, as it adds considerably to the stillness of the fixture 
and provides a much better bearing for the work-support than the 
gear blanks themselves. 

Method of Holding Plate-clutch Disks 

A good example of a case where grouping of blanks can be practiced 
with success is shown at A and B in Fig. 62. The work being held is 
disks for plate clutches. These are comparatively thin disks so that 



Fig. 63— A —Method of Holding Automobile Transmission Gears 

Having One Extended Hub 

B —Method of Holding Automobile Transmission Gears 
with Both Hubs Extended 

any inaccuracy between the hole and the face would not affect the 
clamping of the disks. The only objection to this method would be 
where the disks vary considerably in thickness throughout their cir¬ 
cumference. Owing to the use, however, to which these disks are to 
be put, a slight variation does not seriously affect their efficiency. 
A shows a method of mounting disks for cutting teeth on the external 
surface. Here it will be noticed that an arrangement somewhat 
similar to that shown in Fig. 61 is used, the fixture being provided 
with an extended shank for centrally locating the blanks. The 
latter are then clamped down onto the faceplate by means of the top 
plate, the entire fixture being located by the work-arbor. 





















































































































7 ° 


HOLDING AUTOMOBILE TRANSMISSION GEARS 



Fig. 64— A —Method of Holding a Direct-drive Automobile Transmission 

Pinion Having a Long Shank 

B —Method of Holding a Direct-drive Automobile Transmission Pinion 
Having a Comparatively Short Shank 

/?, in Fig. 62, shows a method of holding plate-clutch disks when 
cutting teeth on the interior surface. Here, the faceplate forms a 
pot-type of fixture to receive the disks which are clamped in place by 
a ring, having elongated holes that facilitate its quick removal. A 
series of holes is drilled around the lower portion of the fixture to 
facilitate the removal of oil and chips from the locating surfaces. 

Method of Holding Automobile Transmission Gears 

The methods used in holding automobile transmission gears are 
governed almost entirely by the character and shape of the gears. 
There are two common types of automobile transmission gears— 
those having square and those having splined holes. Bushings are 
used to fit the square holes and a smaller work-arbor than the hole in 
the gear blank is then necessary. When the hole in the gear blank 
is so small that the use of a bushing would weaken it too much; then 





























































































































HOLDING SHANK GEARS 


7 i 


the arbor is made to fit the hole in the gear. The contour of the gear 
also varies considerably; for instance, the sliding gear is provided 
with an extended boss in which a groove is cut for the shifting fork, 
see A , Fig. 63, where the commendable way of holding gears of this 
type is also shown. The faceplate is machined as illustrated, to 
receive the extended boss of one gear, and then the flat face of the 
other gear brought in contact with the corresponding flat face of the 
lower gear. The top plate is also machined to receive the extended 



Fig. 65— A —Method of Holding a Long Shank Pinion on the 

No. 64 Gear Shaper 

B —Method of Holding a Comparatively Short Shank Pinion 
on the No. 64 Gear Shaper 





























































































































































































72 


HOLDING SHANK GEARS 


boss of the upper gear. For location purposes, bushings are used. 
The lower bushing should extend through one gear and into the 
second one in order to preserve the alignment of the two gears. Using 
a fixture of this type enables the gears to be held accurately and 
rigidly. 

A somewhat similar method of holding is shown at B , in Fig. 63. 
In this case, both hubs extend past the face or rim of the gear, and in 
order to secure the necessary rigidity, it is preferable to use a spacing 
washer between the gears, so as 
to bring their bosses out of con¬ 
tact and support the gear blanks 
at the rims. In this way, the cut¬ 
ter can be made to work on the 
“pull” stroke, and the two gears, 
arbor, faceplate, etc., can be ac¬ 
curately held against the thrust 
of the cut. In both cases in Fig. 

63, it is preferable, of course, to 
use the work-support, as illustrat¬ 
ed, this bearing on the top face of 
the top plate. 

Molding Shank Gears in 
Floating Fixtures 

Two methods of holding auto¬ 
mobile drive-shaft pinions having 
extended shanks are shown in Fig. 

64. In both cases floating types 
of fixtures are used. The method 
shown at A illustrates a floating 
fixture being used for supporting 
a pinion having a comparatively 
long shank. A hardened and 
gr ound bushing fitted into the low¬ 
er end of the work-spindle is used 
for locating the work at the lower 
end; this taking the place of the regular work-arbor. The shank of the 
pinion is then made to pass down through this bushing and is central¬ 
ized at the lower end. I he floating fixture is fastened to the work- 
spindle by means of four fillister-head screws and carries a hardened 




CLAMPING 

BOLT 


CLAMPING 

WASHER 



Fig. 66—Method of Holding an 
Internal Gear Having a Long 
Shank 









































































HOLDING SHANK GEARS 


73 


and ground bushing. This bushing is provided with a shoulder, as 
illustrated, and the lower face of the pinion blank rests on it. 

The pinion is held in the floating fixture by means of a headless- 
screw which presses against a segment brass shoe. In cutting a gear 
blank of this type, the pinion should be placed in the fixture and then 
the fixture and pinion trued up by means of an indicator. After the 
fixture has been trued up it is clamped in position. Owing to the 
character of the fixture used, the “push” stroke is preferable, not 
only because of the lack of clearance space at the bottom of the pinion 
face, but also because of the fact that if the “pull” stroke were used, it 
would have a tendency to pull the pinion out of the fixture. 

I he method shown at B differs only in a few minor details from 
that at A. In this case no bushing is used in the work-spindle, 
because of the comparatively short shank on the pinion. The 
floating-fixture principle is adopted and the cutter operated on the 
“push” stroke. 

Holding Shank Gears on No. 64 Gear Shaper 

The design of the pinions illustrated at A and B , in Fig. 64, were of 
such shape that a Gear Shaper having a standard work-spindle could 
be used. Illustrations A and B , Fig. 65, show cases where it is 
necessary to use the largest work-spindle, viz., that used in the No. 64 
machine. A somewhat more elaborate fixture is also adopted. 
Reference to A, Fig. 65, will show that the pinion is not in this case 
supported in a floating fixture, but instead is located by means of 
accurately ground bushings from the journals on which it will subse¬ 
quently rotate. The shank extends clear down to the lower end of 
the spindle, and is supported at the lower end by means of a shoulder 
bushing, fitted into a second bushing, that is made to suit the bore of 
the large work-spindle. A somewhat similar arrangement is used 
at the top end of the work-spindle. The top bushing, however, is 
split into two pieces to facilitate loading the work in the machine. 
For clamping purposes, a through bolt is used; this is fastened at the 
lower end to a plate, which, in turn, is attached to the lower end of 
the work-spindle, and at the upper end holds the work by means of a 
collar and nut. The lower end of the through bolt is pinned to the 
plate to prevent it from turning, and the work is removed by un¬ 
screwing the nut and washer at the top end. To remove the work, 
it is pulled directly up out of the work-spindle, after the apron has 
been swung open. The lower bushing is attached by screws, as il- 


74 


HOLDING INTERNAL SHANK GEAR 


lustrated, to the lower plate. In this case, the work is rigidly clamped 
down against the bushing in the work-spindle and the latter is tied 
to the lower plate, so that the “pull” stroke can be effectively used. 

B shows a somewhat similar arrangement in one respect, but it 
differs slightly in another. In this case, the gear is of such design 
that there is not sufficient clearance for the cutter to work on the 
“pull” stroke; hence it is not necessary to provide for the “pull” of 
the cutter. The construction is, therefore, reversed, and the work 
supported directly in a bushing clamped to the work-spindle. For 
clamping purposes, a through bolt having a head, and keyed to the 
lower plate is used. This plate in turn is fastened to the lower end 
of the bushing. The work is held by means of a nut and split washer, 
as illustrated. 


Method of Holding an Internal Shank Gear 

Fig. 66 shows an interesting method that is used for holding an 
internal gear having an extended shank, the fixture being adapted to 
the No. 61 Gear Shaper; this machine has a work-spindle provided 
with a 2 7 /g inch hole. Carefully ground bushings are inserted into 
the lower and upper ends of the work-spindle, and in addition, the 
top of the work-spindle is provided with a carefully machined face¬ 
plate. The work is held by a draw bolt that is made to fit the lower 
threaded end of the work, the latter being held down tightly against 
the faceplate by means of a nut and split washer. The construction 
of this fixture is such that the work is clamped rigidly to the work- 
spindle, preventing any shifting of the work, and also holding it 
accurately while the cutter is at work. Owing to the design of the 
gear, the machine is operated on the “push” stroke and the hub type 
of cutter used. 

Method of Holding Automobile Cluster Gears 

The countershaft gear used in an automobile three-speed forward 
and reverse type of gear box is in most cases made in one piece. 
There are several forms in which this gear is made, and Fig. 67 shows 
one form which has four gears made integral. The cluster-gear unit, 
when in use, is held on a shaft that generally rotates on ball bearings; 
or it is held rigidly and the gear blank provided with bronze bushings. 
The hole of the gear blank is, therefore, the axis upon which it rotates, 
and hence the point from which it should be located and held when 
the teeth are being cut. Three settings are necessary to finish this 


HOLDING AUTOMOBILE COUNTERSHAFT GEARS 75 

cluster gear. In the first setting, shown at A, the two smaller gears 
are finished, and owing to the shape of the work, the cutter, which is 
of the thin-web type, is operated on the “push” stroke. The work 
is located centrally by means of the work-arbor and is supported by a 
special faceplate machined to receive one end of the gear, the rim of 
the largest gear resting on the top face of the faceplate. 



Fig. 67—Methods of Holding Cluster-gear Blanks 


In the second setting, shown at B, the cutter is reversed on the 
spindle and operated on the “pull” stroke, the same type of fixture 
being used, as that illustrated at A. It is preferable when machining 
the gear blank on the “pull” stroke, as illustrated at B , to use the 
work-support, so as to overcome any liability of springing the work- 
arbor. This support is located outside the plane in which the cutter 
works, and hence does not interfere with it. 

C shows the final setting for finishing the fourth gear. In this 
case, also, the “push” stroke is used similar to A , and owing to the 
clearance between the shoulder, the thin-web type of cutter is used. 

Another type of cluster gear for an automobile, which differs con- 



























































































































7 6 


HOLDING CLUSTER GEAR 


siderably in construction from that illustrated in big. 67 is shown in 
Fig. 68. In this case, the three gears are integral with the shaft, so 
that a different method of mounting is necessary. I he fixture used 
comprises a special faceplate, which is located centrally by means of a 
special work-arbor, that is machined as illustrated to clear the pro¬ 
jecting end of the shaft. The work is held to the faceplate by means 
of four cap-screws, and is supported at the upper end by a hardened 
and ground bushing fitting the opposite end of the shaft. This 
support is in the form of an arm carried on a special bracket, which 



Fig. 68—Method of Holding and Supporting One-piece Cluster Gear 


at the lower end forms the apron cover. This lower portion of the 
bracket is held by screws to the work-spindle, and is additionally 
supported and clamped by a through bolt passing through the hole 
ordinarily occupied by the support in the apron. The arm is held on 
the stud, the lower end of which is provided with annular gear teeth, 
and it is supported at the rear end by means of a stud fitting in a 
hardened and ground bushing. 

In order to facilitate the quick removal of the work, the supporting 
























































































































































HOLDING WORK ON CENTERS 


77 


arm can be quickly elevated by means of a handle that is placed on 
the stud projecting from the support and carrying on its other end 
an integral pinion. This pinion in turn meshes with the annular 
gear teeth cut on the supporting stud, and rotation of the pinion in a 
right-hand direction elevates the entire arm, enabling the work to be 
removed from the fixture after the cap-screws are removed. The 
center gear is cut with the machine operating on the “push” stroke, 



Fig. 69—Method of Holding Work on Centers 


and the lower and upper gears, with the machine operating on the 
“pull” stroke. Owing to the rigid manner in which the work is 
supported, it is possible to use either stroke in this case, without any 
liability of shifting the work. 

Holding Work on Centers 

In all of the previous examples, the work was located either from 
the external diameter or from the hole. There are certain classes of 
work, however, where it is preferable to hold the work on centers, 

















































































































78 


HOLDING WORK ON CENTERS 


especially when the part on which the teeth are cut is supported in 
that manner when assembled in the machine in which it is to be used; 
or when all of the other important operations have been performed 
with the work held on centers. A case in point, where the center¬ 
holding method is advisable, is shown in Fig. 69. This is a pinion for 
an armature of an electric starter, and owing to the construction ol 
the pinion, it could not be held accurately in any other way except on 
centers; consequently, a special fixture is necessary. 

Before describing the construction of this fixture, it might be 
stated that ordinarily, where possible, the work should not be held 
on centers because of the difficulty generally experienced in preventing 
it from shifting when being machined. It is more difficult, of course, 
to clamp the work on center-points than it is where a greater bearing 
surface is provided. 

The fixture illustrated in Fig. 69 is of a universal character and is 
intended to hold several different sizes and forms of pinions. For 
this reason, the upper support is made adjustable on a special bracket 
which is clamped in the same manner as the fixture illustrated in Fig. 
68. The lower portion ol the fixture consists of a special work-arbor 
provided with a cone-center and on which is screwed a faceplate, 
used for location purposes. This faceplate has a slot cut in one side 
in which a stop or location pin fits, this being backed up by a screw 
to prevent the work from shifting. The collar which carries this stop 
pin is then fastened to the lower end of the pinion by means of a 
headless-screw. In this way, the work is prevented from moving 
when being machined. 

The fixture is also provided with three holes drilled through from 
the lower circumference to the “pocket,” to facilitate the removal of 
oil and chips. The upper part of the fixture, which is in the form of a 
slide, is held by a screw to the bracket previously described. The 
adjustable block carries a bushing in which the upper cone-center fits, 
the latter being acted upon by an adjusting screw. Owing to the lack 
of clearance at the bottom, the “push” stroke is necessary. In 
aligning this fixture properly on the machine a special arbor and 
bushing are used, as illustrated in the detailed view. The special 
arbor is placed in the work-spindle and then a carefully ground 
bushing slipped over the small stem of the arbor. This bushing is 
also a good fit for the upper supporting center and thus effectively 
aligns the bracket with the hole in the work-spindle. The top center 
has to be adjusted each time a piece is located in the fixture. 


FLOATING FIXTURE FOR HOLDING PINIONS 79 

Floating Fixtures for Holding Internal Pinions 

An interesting type of fixture for holding a sprocket shaft for an 
electric starter in which eight half-holes, instead of regular gear 
teeth, aie to be cut, is shown at A in Fig. 70. The fixture consists of 
a faceplate which is screwed to a special arbor, the function of the 
faceplate is to hold the work-arbor up in the work-spindle, and in 
addition to center the fixture in which the work is clamped. The 
fixture used is of the “floating” type and is clamped to the faceplate 
by four screws. The work is fitted into a carefully hardened and 
ground bushing and is held in place by a segment brass shoe, acted 


CUTTER-SPINDLE 


-SPECIAL SHANK CUTTER 
-SPROCKET SHAFT BLANK. 



-WORK-SPINDLE ■ 


mm 


APRON-QUILL 


CUTTER-SPINDLE 


CLAMPING 
RING 



Fig. 70— A —Method of Holding a Small Internal Pinion 
B —Method of Holding a Coupling Pulley for an Electric Starter 


upon by a headless set-screw. Owing to the small hole in the work 
where the “teeth” are to be cut, a shank-type of cutter is neces¬ 
sary. 

A somewhat similar type of fixture to that illustrated at A is shown 
at B. In this case, however, the fixture is used for holding a coupling 
pulley for an electric starter. This part also is to be machined with 
eight half-holes, and is supported directly by the work-arbor, which 
is provided with an extended shank fitting the hole in the work. 
The work is clamped to the faceplate by a circular clamping ring and 





















































































































































8o 


HOLDING INTERNAL GEAR RINGS 


three bolts. It will also be noticed that in this case the shank-type 
of cutter is used. 

Fixture for Holding Internal Gear Rings 

A fixture for holding internal gear rings is shown in Fig. 71. This 
fixture comprises a large casting made in the form of a wheel, the hub 
part of which fits over the work-arbor and is clamped to it as illus¬ 
trated. For an additional support, the fixture is also fastened by 
four screws to the top face of the work-spindle, and at its rim, practi¬ 
cally directly beneath where the cutting is done, it is supported by 
means of the roll-support held in the apron. The work, which is an 



internal-gear ring, is held two at a time in the fixture against a 
machined seat by eight straps. These straps, in turn, are acted upon 
by bolts and located beneath them are springs to assist in removing 
them from the work once the bolts are released. The straps are 
provided with elongated holes, so that to remove the work it is only 
necessary to release the bolts, pull back the straps and then lift the 
gear rings out of the fixture. With work of this size and type, of 
course, it is necessary to open the apron to remove and replace the 
work. 

It is advisable in using a fixture of this character, to use a test 
indicator for determining if the inside locating surface of the fixture 
is true with the axis of the work-spindle. If this is not the case, it 
is impossible to cut rings in which the pitch circle of the teeth are 
concentric with the external diameter. 

































































































HOLDING TRACTOR INTERNAL DRIVE GEAR 


81 


Fixture for Holding Tractor Internal Drive Gear 

Another special fixture, which in this case is used for supporting 
and holding a large internal drive gear for a tractor is shown in Fig. 72. 
The fixture differs slightly from that shown in Fig. 71, chiefly in the 
construction of the lower portion. The work itself has a hub, and 
consequently, the fixture cannot extend above the lower surface of 
the hub. Owing also to the large hole in this hub it is necessary to 
make a special bushing to fit the work-arbor and also the hub. The 
fixture consists of an iron casting fastened by four screws to the top 
face of the work-spindle, and having a machined ledge on which the 
work is clamped by eight clamping bolts. The outer rim of the 



Fig. 72—Fixture for Holding an Internal Drive Gear for a Tractor 


fixture is supported against the thrust of the cut by the roll support 
held in the apron. 

In the fixtures shown in Figs. 71 and 72 it will be noticed that chip 
pans are provided. Owing to the construction of this fixture a chip 
pan is provided in order to facilitate the removal of chips; this pan is 
removed each time a gear blank is taken off, so as to clean out all the 
chips from the fixture. The oil, however, passes through the holes 
in this pan and back to the circulating pump. 

Method of Holding Thin-wall Driving Drum for 

Disk Clutch 

The disk-clutch driving drum shown in Fig. 73 presents a difficult 
holding proposition, because of the thin wall and the consequent 
lack of support. There are several methods that could be used for 





















































































































82 


HOLDING THIN-WALL CLUTCH DRUM 



Fig. 73—Method of Holding an Automobile Disk-clutch Driving Drum 


holding this piece, but the one suggested in Fig. 73 is preferable, 
especially when the external diameter of the drum is not machined 
to an exact size. When the external diameter is machined to close 
limits, then the most rigid support could be obtained by making a 
fixture in which the external diameter of the driving drum was a good 
fit. 

The fixture shown in Fig. 73 is fastened ciirectly by screws, to the 
work-spindle nose, and is additionally supported by the roll support 
held on the apron. The work is held by cap-screws to a machined 
seat in the top part of the fixture, in the same manner as it is clamped 
when in use. The lower end is, therefore, allowed to “float,” and 
once the work is clamped in place, the spring plungers are locked to 
prevent the work from shifting and obviate the liability of chatter. 
Owing to the lack of clearance at the bottom of the fixture, the thin- 
web type of cutter is used. In this particular case four spring 
plungers are provided, and these are so distributed as to support the 
work at points midway between the top and lower ends and at the 
lower edge. 












































































































UNIVERSAL INTERNAL GEAR-HOLDING FIXTURE 8^ 

Universal Internal Gear-holding Fixture 

In the fixtures previously illustrated for holding internal gears, it 
will be noticed that each one of these fixtures was designed particularly 
for the work it was intended to handle. When only a small num¬ 
ber of gears, however, are to be machined it does not always pay to 
design a special fixture, and when this is the case, a universal type 
of fixture similar to that illustrated in Fig. 74 should be used. This 
fixture consists simply of a faceplate which is attached by screws to 
the top face of the work-spindle. Located on this faceplate is a 
centering ring which is held in place by means of straps. To make 
sure that the work is properly located, the holding ring is trued up by 



Fig. 74—Universal Type of Faceplate Fixture 


means of a dial indicator. The work to be machined, which in this 
case happens to be an internal helical gear ring, is the n located by 
means of this centering ring and clamped down by means of straps, 
as illustrated. This makes a simple fixture, easy to operate and one 
that covers a large range of special work. It is a necessary adjunct 
to a gear plant doing jobbing work on the Gear Shaper. It is advis¬ 
able occasionally to test the truth of the top face of this plate and 
when it is found to have become sprung it should be set up accu¬ 
rately in a lathe and re-faced, locating it from the lower surface. The 
holding fixture for the gear being cut, should also be carefully tested 
each time it is set up. This is done, as has been previously men¬ 
tioned in connection with the testing of the work-arbor, Opera¬ 
tion 3-a. 












8 4 


HOLDING AND CLAMPING GEAR BLANKS 


Summary of Important Points on Holding and Clamping 

Gear Blanks 

Mention has previously been made of the care which should be 
exercised in mounting and clamping gears on the Gear Shaper. 
Those accustomed to accurate work know what trouble dirt causes in 
securing accurate gears. It is, therefore, important that the Gear 
Shaper be kept clean, and this remark applies particularly to the 
cutter-spindle, work-spindle, arbor, faceplate and gear blanks. 

Whenever a work-arbor is placed in the work-spindle it should 
always be tested with a test indicator to see that it runs dead true. 
The faceplate should be tested to see that the top surface runs true, 
and the gear blanks should be tested before they are clamped on the 
work-arbor to see that they run true. 

Another important point to look out for is the accuracy between 
the face and the hole of the gear blank. Gear blanks in which the 
face is not true with the hole cannot be accurately held on an arbor, 
and this is particularly true when more than one gear blank is clamped 
on the arbor at one time. 

When the part to be cut on the Gear Shaper is of such shape that a 
special fixture is required, this should be accurately machined and 
accurately indicated on the Gear Shaper before placing the gear blank 
in position. The fixture should be tested to see that the surface 
against which the gear will be clamped runs true. 

In machining gear blanks or other work where the fixture is not 
depended upon to hold the gear accurately, then the gear itself should 
be accurately indicated by a test indicator. The indicator spindle 
should be brought into contact with that surface of the gear, which 
subsequently is used for locating purposes in the machine of which it 
forms a part. 

Too much care cannot be exercised in propery locating and 
clamping gear blanks 


CHAPTER VIE 


Cutting Compounds for Gear Cutting 

The question which decides whether a cooling compound or a 
cutting oil is to be used is dependent entirely upon the nature of the 
material being cut. If the amount of metal being removed generates 
considerable heat, it will require a better cooling medium than can 
be found in the list of oils. On the other hand, it is fairly safe to say 
that the regular soluble oils or cutting compounds, which have a large 
percentage of water in their make-up, are well suited to conditions 
where considerable heat is generated. The better the finish required, 
the more oil will be required in the compound. 

Some materials, such as cast iron, are generally cut dry, and this 
rule also applies to the Gear Shaper for the reason that when a cooling 
compound is used, the fine dust is formed into a paste by the action 
of the coolant; this adheres to the cutting edge of the cutter and soon 
dulls its keen edge. Various combinations are made to obtain cutting 
compounds for machinery and alloy steels, depending upon whether 
the operation is a roughing or a finishing one. These various com¬ 
pounds will be dealt with in detail in the following. It might be 
stated, however, that conditions vary so much that it is impossible 
to state definitely just when a certain compound or cutting oil is 
satisfactory until it has been tried out under actual working condi¬ 
tions. 

Cooling Compounds for Cast Iron 

As a general rule, cast iron is cut dry on the Gear Shaper, no cooling 
compound being used. The reason for this has been previously 
stated. If it were possible to prevent the formation of a paste, the 
speed of the Gear Shaper could be considerably increased when 
cutting cast iron over that used when cutting steel. As a matter of 
fact, however, practically the same speed is used for cutting cast iron 
and steel. When a coolant is used, it is preferable to apply it only on 
the roughing operation and to do the finishing operation dry. 


86 


CUTTING OILS FOR STEEL 


Cutting Oils for Machinery and Soft Steel 

Owing to the “stringy” and soft nature of low-carbon or machinery 
steel, it is sometimes found that the chips cling to the edge of the 
cutting tool and do not cut clean, but tear from the side of the gear 
tooth. This trouble is more noticeable in the case of fine-pitch gears, 
due, of course, to the lack of chip clearance. When a good finish 
cannot be secured with commercial cutting compounds, the trouble 
may be overcome, in most cases, by using mineral-lard oil to which 
sulphur is added. The proportions are one pound of commercial 
sulphur to a Gear Shaper tank full of mineral-lard oil. Cases have 
been found when the steel was so soft that even this compound did not 
bring satisfactory results, and when all other methods of preventing 
extreme tearing have failed, a commercial grade of olive oil has proved 
effective. At the present time, however, this commodity is so ex¬ 
pensive that it should be used only as a last resort. 

Cutting Oils for Alloy and High-carbon Steels 

Alloy steels vary so much in their chemical constituents that it is 
difficult to give any definite information as to the cutting oil or com¬ 
pound that should be used. For automobile gears, an alloy steel 
that is very common is chrome-nickel, the nickel content varying 
from 0.3 to 0.5 per cent. Practice varies considerably in regard to 
whether a cooling compound or a cutting oil should be used. In 
general, however, it will be found that for roughing, a cooling com¬ 
pound is used, and for finishing, a cutting oil; generally mineral-lard 
oil or a comparatively cheap grade of motor oil gives the best results, 
although there are exceptions to this rule. When the steel contains 
from 0.25 to 0.35 per cent carbon, a good commercial finish can be 
secured by the use of commercial soluble cutting compounds; these 
are sometimes mixed with mineral-lard oil when a good smooth 
finish is desired. 

Commercial soluble cutting compounds are generally used in a 
diluted form, the amount of water added being governed by the 
nature of the material being cut. A reduction of 20 per cent is 
generally found satisfactory, although the amount of dilution is also 
dependent upon the constituents of the compound used. For 
finishing, an oil commercially known as No. 1 lard oil is quite exten¬ 
sively used, and this is sometimes diluted with kerosene. Even on 
alloy steels, trouble is sometimes experienced with tearing, especially 
when the carbon content is low, and when this is the case, an addition 


CUTTING COMPOUNDS FOR VARIOUS MATERIALS 


87 


of powdered sulphur to the lubricant will generally bring relief. 

For cutting very hard or high-carbon steel, a water compound is 
not satisfactory, and when trouble is experienced with lard oil or 
mineral-lard oil, it is sometimes possible to improve the cutting 
action by the addition of kerosene, or as a last resort, a mixture of 
kerosene and turpentine. A mixture of kerosene and turpentine is 
used when finishing steel gears that have been heat-treated after the 
roughing operation. 

Cooling Compounds for Brass, Bronze and Aluminum 

Ordinary commercial cast brass is cut dry on the Gear Shaper, 
especially when taking a finishing cut, but for roughing, a soluble oil 
or compound will help to keep the cutter cool; although it will add 
little to its cutting efficiency. The same is true of ordinary bronze; 
although when cutting naval or tobin bronze it is generally found 
necessary to use mineral-lard oil and kerosene to prevent tearing. 

For aluminum a soluble compound is used and instead of adding 
water, kerosene is used. Sometimes the proportion of kerosene to 
the compound is about 50 per cent, the percentage, of course, being 
governed by the constituents of the compound. 

Cutting Fibrous Materials 

Materials such as fiber, rawhide, cloth, micarta, etc., are generally 
cut dry on the Gear Shaper, and owing to the lack of strength of these 
materials, it is advisable to use a dummy gear to support the material 
against the thrust of the cutter. When the cutter is cutting on the 
“pull” stroke, the gear should be located on top of the fiber blanks, 
and when cutting on the “push” stroke, the bottom. 


CHAPTER VIII. 


Gaging and Inspecting Gears 

The importance of careful machining in connection with the pro¬ 
duction of accurate gears has been mentioned in Chapter VI. Inas¬ 
much, however, as the operator is depended upon for production, 
some of the important points in connection with the mounting of the 
gears, etc., do not in all cases receive the attention that they deserve. 
For this reason, it is necessary after machining to carefully inspect 
all gears that must be held to certain manufacturing tolerances. 
There are, it might be stated, several important points to look out for 
in order to secure quiet-running gears, and three of these are described 
in the following. 

The Three Essentials of Quiet-running Gears 

In producing gears which must run together quietly and efficiently, 
three of the important points which must be obtained are: I, con¬ 
centricity; 2, correct center distance; 3, properly shaped tooth curves. 

Concentricity 

If the pitch circle upon which an involute gear rotates is not con¬ 
centric with the axis upon which it rotates, then the gear will be noisy 
in action, because it will bear heavier at one point of its circumference 
than it will at other points, and it will have what might be termed an 
'‘intermittent action.” This causes excessive shocks when the gear 
teeth are going into and coming out of action and results in noisy 
gears. The tolerance for eccentricity is governed entirely by the con¬ 
ditions under which the gears are to be used. In order to avoid 
eccentric gears, the blanks should receive careful attention, and the 
work-arbor or fixture should be tested so that it will hold the gears 
‘true. 

Correct Center Distances 

Theoretically speaking, the center distance is made equal to the 


PROPERLY SHAPED TOOTH CURVES 


89 


sum of the pitch radius of the two gears which are to run together. 
But, to provide for unavoidable imperfections in manufacture, certain 
limits of tolerance are set. The limits used are dependent upon 
several conditions, such as pitch of gear teeth, class of work, and 
whether the center distance is fixed or not. Usually the tolerance 
on the pitch diameter of the gears varies from minus 0.002 to 0.004 
inch for gears of from 16 to 24 pitch, and from minus 0.008 to 0.010 
inch for gears of from 14 to 4 pitch. The center distance varies 
from plus or minus 0.001 to 0.0015 inch for 16 pitch, and plus or 
minus 0.605 inch for 4 pitch. When the backlash between the teeth 
of two meshing gears is too great, the gears are noisy when operated 
under power at high speeds. 

Properly Shaped Tooth Curves 

In order that a gear will run quietly, it is necessary that the in¬ 
volute curves on the teeth be correctly formed. With the Fellows 
Gear Shaper method this is comparatively easy of obtainment, 
because of the fact that the cutter works on the “molding-generating” 
principle, and also because the involute curves of the teeth are 
generated by a grinding process after hardening. If there is too much 
backlash, however, between the worms and the index wheels, so that 
the gear blank and cutter are not rotating in proper unison, it is some¬ 
times possible to produce “drunken teeth”; that is, the involute 
curves are not the same on both sides of the tooth. Correct adjust¬ 
ment of the worms and index wheels, however, as explained in Chapter 
IV will remedy this defect. 

Methods of Testing Concentricity of Cut Gears 

r 

The simplest and most practical method of testing the concen¬ 
tricity of a cut gear, is to rotate it in contact with a “perfect” master 
gear of the same pitch. Several standard types of machines are on 
the market for this purpose. One machine, which is illustrated in 
Fig. 75, consists of a bed carrying two slides in which hardened and 
•ground studs are inserted. Bushings to fit the holes in the gears are 
made to slip over these studs and the cut gear and the master gear 
are then placed on the studs and brought into contact. By rotating 
the two gears together it can be determined by the feel of one gear 
meshing with the other whether the cut gear is concentric or not. 
If the gear is eccentric, then the teeth bear unevenly. 

Another method, and one which probably has a wider application, 


90 


MEASURING CENTER DISTANCES 



Fig. 75—Testing Gears for Concentricity by Rolling in Contact 

with Master Gear 

because it eliminates the necessity for skill on the part of the operator, 
is shown in Fig. 76. Jn this case, the design of the fixture is essen¬ 
tially the same as that previously shown, but instead of determining 
the amount of eccentricity by the feel of the gears, a dial indicator 
is used which determines this amount in thousandths or ten thou¬ 
sandths of an inch, depending upon the amount of magnification 
provided in the indicator. 

Measuring Center Distances 

The simplest way to measure the center distance of two gears which 
are to run together is by placing them on fixed studs spaced the re¬ 
quired distance apart. When a fixture of greater refinement, how¬ 
ever, is desired, one stud can be made adjustable, and set by means 
of master gears, the variation in the cut gears from the masters being 
determined by means of a dial indicator. This latter method is of 
particular value, when the limit system of manufacture is used. 

Conclusion 

By keeping the Gear Shaper in proper adjustment and repair, and 
by using suitable work-holding fixtures, it is possible thereby to 
greatly reduce the amount of spoiled work, and practically eliminate 
the necessity for an extensive inspection. Many Gear Shaper oper- 




MEASURING CENTER DISTANCES 


9 1 


a tors as soon as troubles are experienced with gears, look to the 
cutter, thinking that “it is the root of all evil.” But, the true cause 
generally lies either in improperly machined gear blanks, incorrect 
methods of mounting, or in the improper adjustment of the machine. 
Cases have been found where the lower index wheel was bound so 
tightly that it could be rotated only by power, and not by hand. 
The operator had produced poor gears, and blamed it on the cutter. 
M any instances could be cited where similar conditions have arisen. 
The best advice, therefore, is to look first to your blanks, then to the 
machine, and finally to the cutter. Every Gear Shaper cutter is 
carefully ground, inspected and tested before it leaves our plant, and 
every test possible is made in order to eliminate any inaccuracy 
which would affect the quality of the gears produced by it. Some¬ 
times a gear cut with the Gear Shaper cutter is found to have one or 
more thick teeth. This is invariably caused by a cracked cutter. 
The crack may not be noticeable, without the aid of a magnifying 
glass, when it is removed from the spindle, but the pressure exerted 
on it in clamping opens the crack. Cracking of the cutter is generally 
caused by using improper washers, see Chapter IT. 



Fig. 76—Gear Testing Fixture Using Dial Indicator for Testing 

Concentricity of Cut Gears 













92 


GAGING AND INSPECTING GEARS 


Summary of Important Points on Gaging and 
Inspecting Gears 

If the points enumerated in connection with Chapter VI are care¬ 
fully observed, and the gear accurately indicated for cutting, in¬ 
spection of gears after cutting will be greatly reduced. The chief 
reason why inspection of gears is necessary is to ascertain if the 
machining operations have been properly conducted. If the neces¬ 
sary care is exercised in cutting gears, inspection then becomes 
practically unnecessary. 

The requirement which takes first place in the cutting of gears is 
that of concentricity between the hole in the gear blank and the pitch 
circle of the teeth. Eccentric gears are noisy and inefficient. Gears 
in which the teeth are unevenly spaced are also noisy, because of the 
fact that each tooth does not bear its share of the load. 

The necessity, therefore, for accurate gears in which the hole is 
concentric with the pitch circle of the teeth is very important. 

The question of properly shaped tooth curves is not a serious 
difficulty on the Gear Shaper, because of the fact that the Gear 
Shaper cutter works on the “molding-generating” principle and 
generates the involute curves of the teeth. Also the involute curves 
of the cutter teeth are ground theoretically correct after hardening,, 
thus removing all distortion due to the hardening operation. 

One trouble which is sometimes experienced, is that of producing 
thick and thin teeth, this sometimes happening so that one tooth in 
the gear is considerably thicker than all of the others. Invariably 
this results from a cracked Gear Shaper cutter. The crack may not 
be discernible when the cutter is removed from the work-spindle, but 
a careful examination of the cutter generally proves that it is cracked. 

One of the chief reasons for the cracking of the Gear Shaper cutter 
is the use of improperly shaped washers. If the angle on the washer 
does not correspond to that on the top face of the cutter, it does not 
bear evenly and hence exerts an unequal pressure, causing the cutter 
to crack. In this connection, the operator is again referred to 
Chapter II, where the subject of the proper mounting of the Gear 
Shaper cutter is dealt with in detail. 


CHAPTER IX. 


Rules and Formulas 


The following chapter includes rules and formulas for calculating 
change gears for use on the Gear Shaper; rules for calculating produc¬ 
tion; and in addition, rules and formulas for calculating the elements 
of gear teeth. 

Formula for Calculating Change Gears 

When it is desired to cut a gear having a different number of teeth 
from that given in the chart, which is reproduced in Table I, the 
change gears to use can be found by means of the following formula: 

No. of Teeth in Cutter A 

No. of Teeth in Gear ^ No. of Teeth in “Pitch Gear” 


X 



5 

3 


i 

i 


In which: A= Change Gear on Worm-shaft 

B = Change Gear on Quadrant-stud 
C= Change Gear on Lower Shaft 

— = Ratio between Upper and Lower Index Wheels 

3 

Example —Given a gear to cut having 6o teeth and a cutter having 
30 teeth, the “pitch gear” to use would have twice the number of 
teeth of that in the cutter, or 60 teeth. Then to find gears A , B , and 
C , we put these known factors in the formula and solve it by can¬ 
cellation, thus:— 


A B s A B 1 A*B 

7- X — X — X = - X — X - = — 

60 60 C 3 24 C 3 7 lC 





94 


FORMULAS FOR CALCULATING PRODUCTION 


Now, assume any number of teeth for C that is found in the Change 
Gear Chart, say 60 teeth. 

Then: 

AxB Ax B i 
72x60 4320 1 

It is now necessary to find two gears having a number of teeth, 
which when multiplied together will give 4320. It should be stated 
here that in all cases when the number of teeth in the gear to be cut 
exceeds that of the number of teeth in the cutter, gear A should have 
a smaller number of teeth than gear C; therefore, it is necessary to 
find a gear having a smaller number of teeth than 60 which is equally 
divisable into 4320. Try 50 teeth; then 4320-4-50=86 and a fraction. 
We will now try 48; then 4320-4-48 = 90. There are, of course, other 
numbers that we could have used, but as this divides evenly, and 
gears having 48 and 90 teeth, respectively, are supplied with the 
machine, we select the numbers given. "The change gears to use for 
cutting this gear are: “Pitch gear,” 60 teeth; gear A, 4-8 teeth; gear 
B, 90 teeth; gear C, 60 teeth. 

Formulas for Calculating Production 

The first step in calculating the production is to decide on what 
speed (strokes per minute) to run the machine. Reference to Table 
I will give the operator information on this point. The next point 
is the feed. This also is explained in Table I. After the speed and 
feed of the machine have been decided upon, the next step is to 
calculate the time in minutes required for the cutter to feed in to 
depth. 'This is found by means of the following rule and formula: 

The time in minutes required to feed in to depth is equal to the 
whole depth of the tooth in the gear, divided by the product ob¬ 
tained by multiplving the strokes that the machine makes per minute 
by 0.0018 inch, this constant being the depth to which the cutter 
is fed in per stroke of the Gear Shaper; or expressed as a formula: 


W 

t = - 

0.0018x<.V 

In which t =time in minutes required to feed in to depth 
IV = whole depth of tooth in gear 

= strokes of Gear Shaper per minute 





FORMULAS FOR CALCULATING PRODUCTION 95 

I he time in minutes for the gear blank to make one complete 
revolution is determined by the following rule and formula: 

Rule: The time in minutes required for the gear blank to make 
one complete revolution is equal to the product obtained by multiply¬ 
ing the strokes that the machine makes per inch of the pitch diameter 
of the gear blank (see Table III), by the pitch diameter of the gear 

Table III.—Strokes of Gear Shaper per Inch of 
Pitch Diameter of Gear Being Cut 


Diameter of 
Cutter in 
Inches 

Fine 

Medium 

Coarse 

Strokes per Inch of Pitch Diameter of Gear Blank 

1 

1390 

955 

7 21 

2 

695 

477-5 

360.5 

3 

463.3 

3 * 8-3 

240.3 

3-5 

397 - 1 

272.8 

206 

4 

347-5 

238.8 

180.2 


blank; divided by the strokes of the Gear Shaper per minute; or ex¬ 
pressed as a formula: 


sxD 
T= — 

S 

In which T=time in minutes required for the blank to 

make one complete revolution 
s = strokes of machine per inch of pitch diameter 
of gear being cut (see Table III) 

D = pitch diameter in inches of gear being cut 
S = strokes of Gear Shaper per minute 

Example —Assume that it is desired to know, approximately, the 
time required to cut a cast-iron gear blank of 6-pitch, having a pitch 
diameter of 8 inches, i-inch face, and using a 4-inch pitch diameter 
Gear Shaper cutter, with the Gear Shaper operating at 200 strokes 
per minute. The requirements are that the gear must have smooth 
and well-finished teeth, and be otherwise considered first class. We 












9 6 


FORMULAS FOR CALCULATING PRODUCTION 


have decided on 200 strokes per minute, and in order to be absolutely 
certain that we will get a fine smooth finish, we will take two cuts 
roughing and finishing—using the medium feed. 

Assume that the gear to be cut is of such shape that we can hold 
three blanks on the work-arbor at one setting, giving a total face 
width of 3 inches, which in this case is about the maximum for 200 
strokes on cast iron. 

Then the time t in minutes required to feed in to depth= 


W = °-375 = Q -375 

0.001 8 x 3 * 0.0018x200 0.360 


1.04 minutes 


The time T in minutes required to make one complete revolution 
of the gear blank = 


sxD 238.8x8 1910.4 

- = - =- = 9.55 minutes for one cut; 

S 200 200 


or 9.55x2= 19.1 minutes for two cuts 

Therefore, the cutting time required to complete the gear taking 
two cuts and using the same feed for each cut is 1.04+19.1 =20.14, 
or reducing this to minutes and seconds = 2o 14 100 minutes or 20 
minutes and 8 J 4 seconds. This is the actual cutting time for three 
gears, the cutting time for one gear will be }/% this or 6 minutes and 
42^ seconds, approximately. 

We have not in this case taken into consideration the time re¬ 
quired to replace and remove the work, set the machine, etc. As 
has been previously mentioned, this is dependent upon the size and 
shape of the work and type of fixture used. The loading and other 
idle time for the average run of work varies all the way from 1/10 
to J A, of the cutting time. In this case the work is comparatively 
simple to load, so we will take 1/10. 1/10 of 20 minutes, 8 Yl seconds 

= approximately 2 minutes. Therefore, the total estimated time 
per gear from floor to floor is 8 minutes, 42J4 seconds, or approxi¬ 
mately 9 minutes. 

Rules for Calculating Elements of Gear Teeth 

Frequently it is necessary that the operator of a Fellows Gear 
Shaper should know how to calculate some of the principal elements 
of gears, such as the diametral or circular pitch, center distance, etc. 








FORMS OF GEAR TEETH 


97 


The present chapter has been prepared with the hope that the 
operator will get the necessary information in order to enable him to 
make some of the simplest calculations. An endeavor has been made 
to eliminate as far as possible the use of formulas, and instead, use 
rules which do not appear so difficult to understand. For the use of 
those who prefer a formula to a rule, Table IV has been included. 

Systems for Calculating Elements of Gear Teeth 

As is common to all linear measurements, there are two systems 
in use for calculating the elements of gear teeth, viz., the English and 
the Metric. With the English system, the various elements are 
based on the diametral pitch, which is used in the form of a ratio and 
is found by dividing the number of teeth in the gear by its pitch 
diameter. 

With the Metric system, the diametral pitch is not used, but in¬ 
stead, the dimensions of the gear teeth are expressed by reference 
to the module of the gear. The module is equal to the pitch diameter 
in millimeters divided by the number of teeth in the gear. The ratio, 
therefore, used with the Metric (module) system is just the reverse 
of that used in the English system. In one case, the ratio is equal to 
the pitch diameter divided by the number of teeth in the gear, and 
in the other, the number of teeth in the gear divided by the pitch 
diameter. 

Forms of Gear Teeth 

There are several forms of gear teeth, but only two are in common 
use, viz., the standard 14^-degree involute tooth and the stub tooth. 
The standard involute tooth has a pressure angle, or angle of obliquity 
of 14^ degrees; hence, the rack meshing with gears cut according to 
this standard have straight sides inclined 14)^2 degrees from the 
vertical; or an included angle of 29 degrees. 

The stub tooth is a modification of the standard involute tooth, 
developed by the Fellows Gear Shaper Co., in 1899, and is now 
almost universally adopted for gears used in automobiles, trucks, 
machine tools, and many other mechanisms employing gears for 
power transmission purposes. The stub tooth has a pressure angle 
of 20 degrees, instead of 14^ degrees, and has a shorter addendum 
and dedendum, thus giving greatly added strength to the tooth. 
It is based on two diametral pitches, the first, say six, being used as 
a basis for obtaining the dimensions for the thickness of the tooth, 
number of teeth, and the pitch diameter; while the other, say eight, 


9 8 


RULES AND FORMULAS 


Table IV.—Rules and Formulas for Calculating 
Dimensions of Diametral Pitch Gears 


Rule 

No. 

Dimension 

Wanted 

Rule 

Formula 

1 

Circular 

Pitch. 

Divide 3.1416 by Diametral Pitch. 

3.1416 

V ~ P 

2 

Circular 

Pitch. 

Multiply Pitch Diameter by 3.1416 and divide.. 
Product by Number of Teeth. 

D X3.1416 

P ~ N 

3 

Diametral 
Pitch. 

Divide 3.1416 by Circular Pitch. 

p 3.1416 

V 

4 

Diametral 
Pitch. 

Divide Number of Teeth by Pitch Diameter. 

P- N 

D 

5 

Pitch 

Diameter.. 

Divide Number of Teeth bv Diametral Pitch. 

b 

II 

6 

Pitch 

Diameter.. 

Multiply Number of Teeth by Circular Pitch and 
divide Product by 3.1416. 

N Xp 

3.1416 

7 

Center 

Distance. . 

Add Number of Teeth in Gear and Pinion, and 
divide Sum by Twice Diametral Pitch. 

N +n 

2 P 

8 

Center 

Distance. . 

Multiply Sum of Number of Teeth in Gear and 
Pinion by Circular Pitch, and divide Product 
by 6.2832. 

(AT + n)p 
6.2832 

9 

Addendum... 

Divide 1 by Diametral Pitch. 

1 

° P 

10 

Addendum... 

Divide Circular Pitch by 3.1416. 

V 

3.1416 

11 

Clearance.. .. 

Divide 0.157 by Diametral Pitch. 

0.157 

C P 

12 

Clearance.... 

Divide Circular Pitch by 20. 

c- P 

20 

13 

Whole Depth 
of Tooth.. . 

Divide 2.157 by Diametral Pitch. 

2.157 

w= -—- 

p 

14 

Whole Depth 
of Tooth... 

Multiply Circular Pitch by 0.6866. 

w— p X0.6866 

15 

Thickness of 
Tooth. 

Divide 1.5708 by Diametral Pitch. 

1.5708 

P 

16 

Thickness of 
Tooth. 

Divide Circular Pitch by 2. 

r 2 

17 

Outside 

Diameter.. 

Add 2 to Number of Teeth, and divide Sum by 
Diametral Pitch. 

ob-7 

18 

Outside 

Diameter.. 

Multiply Sum of Number of Teeth plus 2 by 
Circular Pitch, and divide Product by 3.1416.. . 

0 D- <f +11* 

3.1416 

19 

Outside 

Diameter.. 

Add Two Times the Addendum to the Pitch Di¬ 
ameter. 

0 D= D +2a 

20 

Number of 
Teeth 

Multiply Pitch Diameter by Diametral Pitch.... 

N= D XP 

21 

Number of 
Teeth. 

Multiply Pitch Diameter by 3.1416, and divide 
Product by Circular Pitch. 

Ar DX 3.1416 

V 

22 

Number of 
Teeth. 

Multiply Outside Diameter by Diametral Pitch 
and subtract 2 from Product. 

N= (0 D XP)— 2 

23 

Root 

Diameter.. 

Subtract Two Times the Whole Depth from Out¬ 
side Diajneter. 

R D= 0 D —2 w 

24 

Involute 

Base Circle 
Diameter.. 

Multiply Pitch Diameter by Cosine of Pressure 
Angle. 

B= D XCos. a 

■ 1 











































































































































NAMES OF ELEMENTS OF GEAR TEETH 


99 


is used for obtaining the dimensions for the addendum and dedendum. 
A stub tooth, therefore, denoted as 6/8 pitch would have a length of 
tooth equal to an 8-pitch gear, and a circular pitch equal to a 6-pitch 
gear. 

Names of Various Elements of Spur Gear Teeth 

Fig. 77 shows a gear and pinion in mesh of iqj^-degree involute 
tooth torm. 1 he notations on this gear and pinion indicate the 



various elements of a gear tooth, and the following gives a concise 
explanation of the various terms used: 

Outside diameter ( 0 . D.) is the diameter measured over the tops 
of the gear teeth. 

Root diameter ( R . D.) is the diameter measured at the bottom or 
over the root of the gear teeth. 

Center distance ( C) is the distance between the centers of two mesh¬ 
ing gears, or the sum of the pitch radii of the two gears, which are 
tangent to each other. 

Diametral pitch (P ) is the number of teeth for each inch of pitch 
diameter , and is found by dividing the number of teeth by the pitch 
diameter. 


> 

> > 
J 3 
> > > 


) 

> 


) 


» 






























































IOO 


NAMES OF ELEMENTS OF GEAR TEETH 


Circular pitch (p) is the distance from the center of one tooth to the 
center of the next, measured along the pitch circle —on the arc, and 
not in a straight line. 


Table V.—Chordal Tooth Thickness and Corrected 
Addendum for Gears of one Diametral Pitch 


i 



No. of Teeth 
in Gear 

Chordal Tooth 
Thickness, t 

Corrected 
Addendum, H 

Correction, h 

12— 13 

1.5663 

1.0514 

0.0514 

14 — 16 

1.5675 

1.0440 

0.0440 

17— 20 

1.5686 

1.0362 

0.0362 

21— 25 

1.5694 

1.0294 

0.0294 

26— 34 

1.5698 

1.0237 

0.0237 

35— 54 

1.5702 

1.0176 

0.0176 

55—*34 

1.5706 

1.0112 

O.OI 12 

* 35 — 

1.5707 

1.0047 

0.0047 


Chordal pitch (see illustration accompanying Table V), is the dis¬ 
tance from the center, on the pitch circle , of one tooth to the center 
of the next tooth, measured along a straight line. 

Thickness (T) is generally understood to be the thickness of the 
tooth at the pitch circle measured along the circular arc. 




( 


c 


< 


c 

c 

< < 

<■ (, 

< c < 
c 











































RULES FOR CALCULATING GEAR TOOTH PARTS 


IOI 


Chordal thickness , t (see illustration accompanying Table V), is the 
thickness at the pitch circle measured along a straight line, or on the 
chord see chordal pitch. Note: This dimension is controlled by the 
amount of backlash that is found necessary between the teeth of 
mating gears. 

Addendum ( a ) is the distance from the pitch circle to the top of the 
tooth. (See Fig. 77.) 

Dedendum (d) is the distance from the pitch circle to the clearance 
and is equal to the addendum. (See Fig. 77.) 

Working depth (JV) is the depth to which the teeth of one gear enter 
into the spaces between the teeth of the mating gear. 

Clearance (c) is the amount by which the tooth space is cut deeper 
than the working depth of the tooth. 

Face is that part of the tooth curve extending from the pitch circle 
to the outside diameter or circumference. 

Flank is that part of the working depth of the tooth which is located 
inside or below the pitch circle. 

Fillet (f) is the rounded corner where the flank of the tooth runs 
into the bottom of the tooth space. 

Rules for Calculating Elements of Involute 
Gear Teeth 

The following rules, which are presented in formula style in Table 
IV, are used for determining the various elements of a gear tooth. 

Circular Fitch —The circular pitch is seldom used at the present 
time in connection with the calculating of cut gears, and has been 
replaced almost universally by the diametral pitch. The circular 
pitch is equal to the distance from the center of one tooth to the 
center of the next measured on the pitch circle, and is obtained by 
dividing 3.1416 by the diametral pitch; or by multiplying the pitch 
diameter by 3.1416, and dividing the product by the number of 
teeth. Circular pitch is a measurement and is always expressed in 
inches or millimeters. 

When the diametral pitch is known, the circular pitch is found by 
dividing 3.1416 by the diametral pitch. Rule No. /. 

Example —What is the circular pitch when the diametral pitch is 8 ? 

= 0.3927 inch, circular pitch 


8 



102 


RULES FOR CALCULATING GEAR TOOTH PARTS 


When the pitch diameter and the number of teeth in a gear are 
known, the circular pitch can be found by multiplying the pitch 
diameter by 3.1416 and dividing the product by the number of 
teeth. Rule No. 2. 

Example —The pitch diameter of a gear is 2.5 inches, the number 
of teeth 20. Find the circular pitch. 


2.5x3.1416 

20 


0.3927 inch, circular pitch 


Diametral Pitch —The relation between the diametral pitch, pitch 
diameter, and the number of teeth is much simpler to understand 
than the relation between the circular pitch and these same quanti¬ 
ties. Diametral pitch is the number ol teeth for each inch of the 
pitch diameter. Diametral pitch is a ratio, which represents the 
relation between the number of teeth and the pitch diameter, and is 
always expressed as such. 

When the circular pitch is known, the diametral pitch is found by 
dividing 3.1416 by the circular pitch. Rule No. 3. 

Example —The circular pitch of a gear is 0.3927 inch. What is 
the diametral pitch? 


- = 8 diametral pitch 

0.3927 

When the number of teeth and the pitch diameter are known, the 
diametral pitch is found by dividing the number of teeth by the 
pitch diameter. Rule No. 4. 

Example —If a gear has 20 teeth, and the pitch diameter is 2.5 
inches, what is the diametral pitch? 


20 

= 8 diametral pitch 
2.5 

Conversion of circular into diametral pitch —If the circular pitch is 
given, and it is desired to find the corresponding diametral pitch, 
this can be found by dividing 3.1416 by the circular pitch. If the 
diametral pitch is known and it is desired to find the corresponding 
circular pitch, this can be found by dividing 3.1416 by the diametral 
pitch. 

Pitch diameter —When the diametral pitch and the number of the 
teeth in the gear are known, the pitch diameter can be found by 
dividing the number of teeth by the diametral pitch. Rule No. 5. 




RULES FOR CALCULATING GEAR TOOTH PARI S 


103 

Example —An 8-pitch gear has 20 teeth. Find the pitch diameter. 


20 

8 


2.5 inches, pitch diameter 


When the circular pitch is known and it is desired to find the pitch 
diameter, the pitch diameter is found by multiplying the number of 
teeth by the circular pitch and dividing by 3.1416. Rule No. 6. 

Example —A gear has 20 teeth, 0.3927-inch circular pitch. Find 
the pitch diameter. 


20x0.3927 . , . , 

-7— = 2.5 inches, pitch diameter 

3.1416 

Center distance —To find the center distance when the number of 
teeth and the diametral pitch of two gears are known, add together 
the number of teeth in both gears and divide the sum by twice the 
diametral pitch. Rule No. 7. 

Example —Find the center distance between two gears of 8 diame¬ 
tral pitch, the number of teeth in one gear being 24, and the other 16. 

— = —: = 2.C inches, center distance 
2x8 16 


To find the center distance when the circular pitch and number of 
teeth in two gears are known, multiply the sum of the number of 
teeth in the two gears by the circular pitch and divide the product by 
6.2832. Rule No. 8. 

Example —The circular pitch of two gears having 24 and 16 teeth, 
respectively, is 0.3927 inch. Find the center distance. 

(24+16)0.3927 L _ ^ 

--- = 2.5 inches, center distance 

6.2832 

Addendum —The addendum of a gear tooth is always in 14H degree 
involute gearing made equal to one divided by the diametral pitch. 
Rule No. 9. 

Example —Find the addendum of a gear of 8-diametral pitch. 


1 

8 


0.125 inch, addendum 





104 


RULES FOR CALCULATING GEAR TOOTH PARTS 


If the circular pitch is given, the addendum equals the circular 
pitch divided by 3.1416. Rule No. 10. 

Example —If the circular pitch is 0.3927 inch, find the addendum. 

0.3927 

-- = 0.125 inch, addendum 

3.1416 

Clearance —The clearance below the working depth of a tooth is 
made equal to 0.157 divided by the diametral pitch. Rule No. //. 
Example —Find the clearance of a gear tooth of 8-diametral pitch. 


Q-I57 

8 


0.0196 inch, clearance 


If the circular pitch is given, the clearance may be found by 
dividing the circular pitch by 20. Rule No. 12. 

Example —Find the clearance of a gear tooth of 0.3927 inch circular 
pitch. 

0 -3927 , . 1 , 

-= 0.0196 inch, clearance 

20 


Clearance of gears cut on the Gear Shaper —When 14^0-degree in¬ 
volute gears are cut on the Fellows Gear Shaper, the clearance is 
made equal to 0.25 inch divided by the diametral pitch. Hence, 
the root diameters of gears cut on the Gear Shaper are smaller or 
less than the root diameter of ordinary milled gears. The pitch 
and outside diameters, of course, are the same as gears made by 
milling cutters or hobs. 

Whole depth of tooth —The whole depth of tooth is equal to twice 
the addendum plus the clearance. It is found by dividing 2.157 by 
the diametral pitch. (2.250 when cut with Gear Shaper cutter.) 
Rule No. 75. 

Example —Find the whole depth of a tooth of 8-diametral pitch. 
2.157 

—— = 0.2696 inch, whole depth of tooth 
8 

If the circular pitch is given, the whole depth of tooth can be found 
by multiplying the circular pitch by 0.6866. Rule No. 14. 

Example —Find the whole depth of tooth for a 0.3927-inch circular 
pitch gear. 

0.3927x0.6866 = 0.2696 inch, whole depth of tooth 






RULES FOR CALCULATING GEAR TOOTH PARTS 105 

Thickness of Tooth —The thickness of the tooth at the pitch line 
measured along the circular arc is found by dividing 1.5708 by the 
diametral pitch. Rule No. 15. 

Example —Find the thickness of the tooth at the pitch line of a 
gear of 8-diametral pitch. 


1.5708 

8 


0.1963 inch, thickness of tooth 


If the circular pitch is known, the thickness of the tooth equals the 
circular pitch divided by 2. Rule No. 16. 

Example —Find the thickness of tooth of an 0.3927-inch circular 
pitch gear. 

0.3927 

= 0.1963 inch, thickness of tooth 


Outside dia?neter —When the diametral pitch is known, the outside 
diameter of a gear can be found by adding 2 to the number of teeth 
and dividing the sum thus obtained by the diametral pitch. Rule 
No. 17. 

Example —Find the outside diameter of an 8-diametral pitch gear 
having 20 teeth. 

20+2 22 

- = — = 2.7c inches, outside diameter 

8 8 

If the circular pitch is given, the outside diameter can be found by 
multiplying the sum of the number of teeth plus 2 by the circular 
pitch, and dividing the product by 3.1416. Rule No. 18. 

Example —Find the outside diameter of a 0.3927-inch circular 
pitch gear having 20 teeth. 

(20 + 2)0.3927 8.6394 . . . . 

- = - = 2.75 inches, outside diameter 

3.1416 3* T 4 l6 

When the addendum and the pitch diameter are known, the outside 
diameter can be found by adding two times the addendum to the 
pitch diameter. Rule No. 19. 

Exa?nple —Find the outside diameter of a gear having a pitch 
diameter of 2.5 inches and an addendum, 0.125 inch. 

2.5 + (o.125x2) = 2.75 inches, outside diameter 







io6 


RULES FOR CALCULATING GEAR TOOTH PARTS 


Number of teeth —To find the number of teeth when the diametral 
pitch and pitch diameter are known, multiply the pitch diameter by 
the diametral pitch and the product will give the number of teeth in 
the gear. Rule No. 20. 

Example —Find the number of teeth in an 8-diametral pitch gear 
having a pitch diameter of 2.5 inches. 

2.5x8 = 20 teeth 

When the circular pitch and the pitch diameter are known, the 
number of teeth can be found by multiplying the pitch diameter by 
3.1416 and dividing the product by the circular pitch. Rule No. 21. 

Example —Find the number of teeth in an 0.3927-inch circular 
pitch gear having a pitch diameter of 2.5 inches. 

3.1416x2.5 

- = 20 teeth 

0.3927 

When the outside diameter and the diametral pitch are known, the 
number of teeth can be found by multiplying the outside diameter by 
the diametral pitch and subtracting 2 from the product. Rule No. 
22. 

Example —Find the number of teeth in a gear of 8-diametral pitch, 
having an outside diameter of 2.75 inches. 

(8x2.75) —2 = 20 teeth 

Root diameter , or the diameter at the bottom of the tooth space, is 
found by subtracting twice the whole depth of tooth from the outside 
diameter. Rule No. 2j. (Note—see clearance of gears cut on 
Fellows Gear Shaper.) 

Example —Find the root diameter of a gear having an outside 
diameter of 2.75 inches and a whole depth of tooth of 0.2696 inch. 

2.75 — (0.2696x2) = 2.21 inches, root diameter 

Involute Base Circle Diameter (B , Fig. 77) is the diameter of a 
circle drawn from the center of the gear that is tangent to the line 
of action, and is the circle from which the involute tooth curves are 
developed. Io find the involute base circle diameter, when the 
pressure angle, or angle of obliquity is known, multiply the pitch 
diameter by the cosine of the pressure angle. Rule No. 24. 



INVOLUTE BASE CIRCLE 


107 

Example —Find the involute base circle diameter of a gear having 
a pitch diameter of 2.5 inches and a pressure angle of 14J 2 degrees. 
(Cosine of 14F2 degrees = 0.9682. Cosine of 20 degrees = 0.9397.) 

2.5x0.9682 = 2.420 inches, involute base circle diameter 

Pressure angle a (angle of obliquity) is the angle formed between 
the line of action and the common tangent, see Fig. 77. Any change 
that is made in the base circle also changes the pressure angle and the 
shape of the involute tooth outline. The pressure angle is generally 
a standard factor such as 14F2 or 20 degrees, and as has been shown in 
Rule No. 24.) is used for obtaining the involute base circle diameter. 

Velocity ratio —The velocity ratio of a pair of gears, or of a gear 
and pinion, may be expressed as the ratio of the number of revolu¬ 
tions which the driving gear makes per minute to the number which 
the driven gear makes in the same time. For instance, if the driving 
gear runs at 200 revolutions per minute and the driven gear at 50 
revolutions per minute, the velocity ratio is 200 to 50 or 4 to 1. 

To find the revolutions per minute of the driven gear, when the 
number of teeth in the two gears is known, multiply the revolutions 
per minute of the driving gear by the number of its teeth, and divide 
the product by the number of teeth in the driven gear. Rule No. 25. 

Example —A gear having 20 teeth and rotating at 200 revolutions 
per minute, drives a gear having 40 teeth, how many revolutions 
per minute does the driven gear make? 

200X20 

- = 100 revolutions per minute 

40 

The pitch point (see Fig. 77), of a pair of gears is the point of 
tangency of the pitch circles. 

The common tangent (see Fig. 77), of a pair of gears is a line passing 
through the pitch point, at right angles to the center line. It is tan¬ 
gent to both of the pitch circles. 

The lines of action (see Fig. 77), of a pair of gears are straight lines 
drawn through the pitch point, each at the same angle with the 
common tangent, and also tangent to the base circle. Contact of 
the teeth can only take place along the line of action. The line of 
contact is that portion of the line of action where the mating teeth 
are in contact with each other. This is shown by the heavy full 
lines in Fig. 77 



io8 


CHORDAL TOOTH THICKNESS 


Chordal Tooth Thickness and Corresponding 
Corrected Addendum 

In measuring the width and height from the pitch line of the teeth 
of gears, two common methods are used. The first and the most 
satisfactory method is to roll two gears in mesh when held on studs 
placed the required distance apart. The second method is to use the 
gear-tooth caliper or a fixed gage. When using the gear-tooth caliper 
or fixed gage, it is necessary to know the chordal thickness (see 
diagram accompanying Table V), and also the corresponding cor¬ 
rected addendum. 

The rule to use for finding the chordal thickness is as follows: 
First, find the angle a (see illustration accompanying Table V), 
which is obtained by dividing 90 degrees by the number of teeth in the 
gear. Then find /, the chordal thickness. This is obtained by 
multiplying the pitch diameter of the gear by the sine of angle a. 
In order to obtain the height H, it is first necessary to find h; this 
equals 1 minus cosine of angle multiplied by the pitch radius R of the 
gear. H then equals a-f-h. 

Expressed as a formula, the above values are found as follows: 


90 



t =2i?xsin.a 
h = R( 1—cosa.) 

H = a ~\~h 

In which: 

a = one-hall the subtended angle of the tooth in degrees 
iV= number of teeth in gear 
t = chordal thickness of tooth 

h = height of arc or difference between addendum a and 
corrected addendum H 
R = pitch radius of gear 
a = addendum of gear tooth 
H= corrected addendum 

Example —Assume that it is necessary to find the chordal thick¬ 
ness /, and corrected addendum H of a 6-pitch standard iqH-degree 
involute gear having 30 teeth, 5-inch pitch diameter, the addendum 
as shown in Table VIII being 0.1666 inch. 


CHORDAL TOOTH THICKNESS 


109 


QO 

a = — =3 degrees, one-half subtended angle of tooth 
30 

t =5xsin.3° = 5x0.05234 = 0.2617 inch chordal thickness 
h — 2+2(1 - cos.3 0 ) = 23/2(1 —0.9986) =0.0035 inch, height of arc 
H— 0.0035 +°-i666 = 0.1701 inch, corrected addendum 

In Table V is given the chordal tooth thickness and corrected 
addendum for gears of one diametral pitch. In using this table for 
14+2-degree involute gears cut on the Gear Shaper, divide the cor¬ 
rected addendum H (for the number of teeth required) by the di¬ 
ametral pitch of the gear. For example, to find the chordal tooth 
thickness of a 32-tooth, 8-pitch gear, divide 1.5698 by 8 =0.1962 inch, 
which is the chordal tooth thickness. The corrected addendum = 
1.0237-^8=0.1279 inch. 

For the stub-tooth gear, the table is used somewhat differently. 
The chordal tooth thickness is found as explained above, using the 
numerator of the fraction for divisor; but in order to find the corrected 
addendum, the “correction” given in the fourth column of the table 
for the required number of teeth is also divided by the numerator 
of the pitch fraction, and the result added to the addendum as given 
in Table V. Rule No.ji. 

For example, what is the chordal tooth thickness and corrected 
addendum of a stub-tooth gear 4/5 pitch having 15 teeth? 

The chordal tooth thickness will be 1.5675-^-4 = 0.3919 inch. To 
find the corrected addendum, divide the correction (for 15 teeth) 
given in the fourth column of Table V, or 0.0440-1-4 = 0.0110 inch 
for the correction. The standard addendum for the pitch as given 
in Table IX is 0.2000 inch. Adding the correction, 0.2000+0.0110 
= 0.2110 inch, corrected addendum. 

The values given in Table V for chordal tooth thickness and cor¬ 
rected addendum, are, of course, only approximate as they cover a 
range of several teeth. When it is desired to know these dimensions 
to an exact figure, the formulas given on the opposite page should 
be used. 



CHAPTER X. 


Rules for Calculating Elements of Internal Gears 

The rules for finding the dimensions of an internal spur gear are 
similar in most cases to those given for external spur gears, except 
for the modifications made necessary by the fact that the center dis- 
tanee of an internal gear is equal to the difference between the pitch 
radii of the gear and pinion instead of their sum. (See Fig. 78.) In 
calculating the addendum and dedendum, the inside diameter of an 
internal gear takes the place of the outside diameter of an external 
gear. The external diameter is, of course, the diameter of the hole 
in the blank. To use a crude expression, an internal gear is simply 
an external gear turned inside out. 

Interference in Internal Gears 

Owing to the interference that results when an internal gear and 
mating pinion are almost of the same size, certain limits have been 
laid down for the size of the pinion. When teeth of standard iq 1 ^- 
degree pressure-angle involute form are used, the difference between 
the numbers of teeth in the pinion and gear should in no case be less 
than 12, and for the stub form of tooth, 7. It might be stated, how¬ 
ever, that there are certain exceptions to this rule when modified 
shapes of teeth are used, but the rolling action is never as good when 
the difference between the numbers of teeth in the pinion and gear 
is less than that stated. 

One exception to the rule just stated is in automobile clutch gears. 
Here the number of teeth in the pinion is the same as the number of 
teeth in the internal gear. In this case, however, as will be more 
fully explained later, the pinion and gear do not rotate in mesh with 
each other, but simply slide back and forth. 

The rules for calculating six elements of an internal gear that differ 
from an external gear are as follows (See 'Fable VI for formulas): 

Pitch diameter —When the addendum and inside diameter of an 
internal gear are known, the pitch diameter can be found by adding 
twice the standard addendum to the standard inside diameter. Rule 
No. 32. 


INTERNAL GEAR RULES 


111 


Table VI.—Rules and Formulas for Calculating 
Dimensions of Internal Spur Gears 


Rule 

No. 

Dimension 

Wanted 

Rule 

Formula 

.32 

Pitch 

Diameter.. 

Add Twice the Addendum to the Inside 
Diameter. 

D=I+ 2 a 


33 

Center 
Distance.. 

Subtract the Number of Teeth in the Pinion 
from the Number of Teeth in the Gear and 
divide Remainder by Two Times Diametral 
Pitch. 

„ N—n 
c = ,p 


34 

Center 

Distance.. 

Multiply Difference between Number of Teeth 
in Gear and Pinion by Circular Pitch and 
divide Product by 6.2832. 

c ( N—n)p 

6.2832 

35 

Inside 

Diameter.. 

Subtract 2 from the Number of Teeth and 
divide Remainder by Diametral Pitch. 

II 

36 

Inside 

Diameter.. 

Subtract 2 from Number of Teeth, multiply 
Remainder by Circular Pitch and divide 
Product by 3.1416. 

J (N-i)p 

3.1416 

37 

Inside 
Diameter.. 

Subtract Twice the Addendum from Pitch 
Diameter. 

I =D—ia 


38 

Involute 

Base Circle 
Diameter.. 

Multiply Cosine of Pressure Angle by Pitch 
Diameter. 

B = DX Cos. a 



Example —Find the pitch diameter of an internal gear having an 
inside diameter 4 inches and an addendum of 0.125 inch. 

4 + (2xo.i25) =4.250 inches, pitch diameter 

Center distance —When the number of teeth in the gear and pinion 
and the diametral pitch are known, the center distance can be found 
by subtracting the number of teeth in the pinion from the number of 
teeth in the gear and dividing the remainder by twice the diametral 
pitch. Rule No. JJ. 

Example —Find the center distance of an internal gear and pinion 
having 60 and 20 teeth, respectively, the diametral pitch being 8. 

60—20 40 . 

- = — = 2.5 inches, center distance 

2x8 16 

When the number of teeth in the gear and pinion and circular pitch 
are known, the center distance can be found by multiplying the 














































iia 


INTERNAL GEAR RULES 


difference between the numbers of teeth , by the circular pitchy and 
dividing the product by 6.2832. Rule No. 34. 

Example —Find the center distance of an internal gear and pinion 
having 60 and 20 teeth, respectively, the circular pitch being 0.3927 
inch. 


(60 —2o)xQ.^927 . , ,. 

----= 2.5 inches, center distance 

6.2832 



Internal Gear and Pinion 


Inside diameter —When the number of teeth and diametral pitch are 
known, the inside diameter can be found by subtracting 2 from the 
number of teeth and dividing the remainder by the diametral pitch. 
Rule No. 35. 

Example —Find the inside diameter of an internal gear having 60 
teeth of 8-diametral pitch. 



























































INTERNAL CLUTCH GEARS 




6o — 2 

—-— = 7.25 inches, inside diameter 

o 

When the number of teeth in the gear and circular pitch are known, 
the inside diaineter can be found by subtracting 2 from the number oj 
teeth , multiplying the remainder by the circular pitchy and dividing 
the product by 3.1416. Rule No. 36. 

Example —Find the inside diameter of an internal gear having 
60 teeth of 0.3927 inch circular pitch. 

(60—2)xo.3927 . . . 

--- = 7.2c inches, inside diameter 

3.1416 

When the addendum and the pitch diameter are known, the inside 
diameter of an internal gear can be found by subtracting twice the 
addendum from the pitch diameter. Rule No. 33. 

Example —Find the inside diameter of an internal gear having a 
pitch diameter of 7.5 inch and an addendum of 0.125 inch. 

7.5 — (2x0.125) = 7.250 inches, inside diameter 

Involute base circle diameter —When the pressure angle and the 
pitch diameter of an internal gear are known, the involute base circle 
diameter can be found by multiplying the pitch diameter by the 
cosine of the pressure angle. Rule No. 38. 

Exa?nple —What is the involute base circle diameter of an internal 
gear of standard 14^-degree involute-tooth form having a pitch 
diameter of 7.5 inches? 

7.5x0.9682 = 7.261 inches, involute base circle diameter 

For 20-degree pressure angle, multiply the cosine of 20 degrees or 
<0.9397 by the pitch diameter of the gear. Rule No. 39. 

Internal Clutch Gears 

Internal clutch gears used in automobile transmissions generally 
are of drum form inside of which is located a series of disks. The 
internal diameter of the drum (which could be called the driving gear), 
and the external diameter of the inner clutch member (which could be 
called the driven gear), are provided with gear teeth. Located 
between these two gears is a series of disks. These are so arranged 
with gear teeth that each alternate disk meshes with the internal gear 




INTERNAL CLUTCH GEARS 


114 


and external gear, respectively. Two forms of teeth are quite 
commonly used, viz., the iqj^-degree involute and the 20-degree stub 
tooth. 

Internal Clutch Gears—Limits for Size of 

In an internal clutch gear, of course, the internal gear has the same 
number of teeth as those on the disks that fit into it, and theoreti¬ 
cally speaking, the pitch diameter of the teeth in the internal gear 
and disk should coincide. From a practical standpoint, however, this 
is impossible; and in actual practice, the pitch diameter of the teeth 
on the disk is made slightly smaller than that of the internal gear. 
The allowance between these two dimensions to provide for sliding 
without excessive backlash or shake varies all the way from 0.002 



Fig. 79—Diagram Illustrating Trimming of Internal Gear Teeth 
and Suggested Method of Increasing Internal 
Diameter to Avoid Interference 


inch to 0.020 inch, depending on the number of teeth and their form. 

In cutting internal clutch gears of small diameter, there are certain 
limitations to the number of teeth that can be cut on the Gear 
Shaper without cutting away the interference points on the teeth of 
the internal gear. Of course, as shown in Fig. 79, if there is no objec¬ 
tion to the trimming of the points of three or four of the teeth of an 
internal gear, which takes place when the cutter is being fed into 
depth, then the number of teeth can be much smaller than when 
cutting the points would be objectionable. As a general rule, 20 
teeth for a stub tooth and 24 teeth for a 14^ involute tooth is the 
limitation of this practice. 
























CUTTING INTERNAL CLUTCH GEARS 115 

Cutting Internal Clutch Gears 

When cutting an internal clutch gear having a small number of 
teeth, the inside diameter of the clutch should be enlarged to the 
base diameter of the gear. This in no way affects the positive action 
or strength of the clutch, because the involute stops at the base line 
and none of the tooth curve below this point is in contact with the 
mating external gear. Furthermore, the clutch has such an excess 
of strength over the other gears of the transmission that the clutch 
teeth could, if necessary, be cut clear down to the pitch line, or even 
beyond without any danger of seriously affecting its strength or posi¬ 
tive action. 

This can be clearly seen by referring to the enlarged diagram, Fig. 
79. In the diagram, line A represents a cord being wound around a 
cylinder marked “base line.” Point B on this line traces the involute 
curve of the tooth. It is evident that the tracing point cannot travel 
below the cylinder upon which it is wound without giving a reverse 
curve and causing interference. The involute curve then ends at 
point C and there is no tooth contact below this point. Metal S is, 
therefore, useless. This useless metal makes tooth cutting more 
difficult, and in order to eliminate the trouble that is experienced 
in cutting internal teeth, it is advisable to bore the internal gear to 
the base-line diameter. 

Smallest Number of Teeth that Can be Cut with the 
Gear Shaper Cutter 

In cutting an internal gear having a small number of teeth, the 
cutter has a tendency to rub on the tooth of the gear when the apron 
is withdrawn. In order to eliminate this, the eccentric roll, see 
Fig. 46, is adjusted out of contact with the backing-off plunger, so 
that the apron is not relieved on the return stroke of the cutter. In 
other words, the apron is locked continuously during the cutting and 
return strokes. 

As has been previously stated, the smallest number of teeth of 
i43/<2-degree form and of standard inside diameter, that can be cut 
without interference is 24, and the relieving roll should be brought out 
of contact with the plunger when cutting 30 teeth or less. \\ hen the 
inside diameter is enlarged to the base diameter of the gear, the 
minimum number of teeth of i43/2-degree form that can be cut with¬ 
out interference is 20, and the relieving roll should be backed away 
from the plunger for 25 teeth or less. 


n6 


CUTTING INTERNAL CLUTCH GEARS 


When cutting teeth of 20-degree stub-tooth form, the minimum 
number of teeth that can be cut without interference when the gear 
is of standard inside diameter, is 23 for 6/8 pitch, 20 for 5/7 pitch; 
and the eccentric roll should be adjusted out of contact with the 
plunger when cutting 27 teeth or less of 6/8 pitch, or 25 teeth or less 
of 5/7 pitch. When the teeth are of 20-degree stub form with the 
inside diameter enlarged to the base diameter , the minimum number 
of teeth that can be cut without interference when of 6/8 pitch, is 20, 
and the roll should be adjusted for 25 teeth or less. For gears of 
5/7 pitch, the minimum number of teeth is 17, and the roll should 
be adjusted for 21 teeth or less. Below 17 teeth, the corners of three 
or four of the teeth are trimmed as indicated in Fig. 79. In cutting 
an internal gear, the cutter is first fed in to full depth and then the 
rotary feed is engaged. 

For further information on the subject of design and cutting of 
internal gears, the reader is referred to our book, entitled “The In¬ 
ternal Gear—Design and Application.” 



CHAPTER XI. 


Rules and Formulas for Helical Gears 

A helical gear, commonly, but incorrectly called a spiral gear, is 
simply a spur gear with the teeth twisted. When this type of gear 
is used for transmitting power from one shaft to another, located in 
a parallel plane, the helix angle of the teeth need only be sufficient 
to provide for continuous helical action. Any more helix angle than 
this is just so much more end thrust to take care of, without obtaining 
any gain in efficiency or quietness of action. 


Advantages and Tooth Action of the Helical Gear 

The chief advantage secured by using a helical tooth in place of a 
spur tooth is that in the helical tooth the line of action is progressive 



Fig. 80—Diagram Illustrating Line of Contact on Spur and 

Helical Gear Teeth 
















































118 GEAR SHAPER STANDARD HELICAL TOOTH 

starting in at the point and terminating at the base line on one tooth 
and just the reverse on the mating tooth; that is, it starts in at the 
base line and runs off at the point on the mating tooth. Fig. 80 
presents in a graphical manner the line of action of a spur tooth as 
compared with that of the helical. By referring to this diagram, it 
will be seen that the line of action of a spur tooth is parallel with the 
axis of the gear; whereas in the helical, it runs off in a diagonal direc¬ 
tion. The helical tooth also has greater strength than a spur tooth 
of the same pitch. 

Gear Shaper Standard Helical Tooth 

The form of tooth which has been adopted as standard for helical 
gears by the Fellows Gear Shaper Co. is the stub form of tooth, which 
was described in Chapter IX. This tooth makes possible the 
adoption of finer pitches for helical gears as compared with the 14}^- 
degree involute form. This has the advantage of reducing the helix 
angle with a consequent decrease in end thrust, while at the same 
time providing for the necessary strength required. For more de¬ 
tailed information on the stub form of tooth we would refer you to our 
booklet “The Stub Tooth Gear.” 

Gear Shaper Standard Helix Angles 

Two helix angles have been adopted as standards, viz., 15 and 23 
degrees; these two angles cover a large range of work. The helix 
angle of a helical gear is controlled by the pitch and width of face. 
In order, therefore, to find the width of face required to give con¬ 
tinuous helical action, when the pitch and helix angle are known, 
multiply the cotangent of the helix angle by 3.1416 and divide the 
product by the diametral pitch. Rule No. 40. 

Example —Find the width of face of a helical gear of 6/8 pitch, 
having a helix angle of 15 degrees. Note :—The numerator of this 
fraction, or 6, is used in finding the width of face. Cotangent of 15 
degrees = 3.732. Cotangent of 23 degrees = 2.3558 

Then width of face = 

3.732x3.1416 . , . 

- - - = 1.9^4 inch, width of race 

6 

When the helix angle and width of face are known, the diametral 
pitch can be found by multiplying the cotangent of the helix angle by 
3.1416 and dividing the product by the width of face. Rule No. 41 . 



HELICAL GEAR DEFINITIONS 


119 

Example —Find the diametral pitch of a helical gear having a face 
width of 1.954 inch and a helix angle of 15 degrees. 

3.1416x3.732 
!-954 

The minimum width of face for continuous helical action in helical 
and herringbone gears is given in Table VII. Reference to the illus¬ 
tration accompanying this table will show that for a herringbone 
gear in which the teeth are matched, the total width of face required 


6 diametral pitch 


Table VII. Minimum Width of Face for Continuous Helical 
Action of Helical and Herringbone Gears 





K-- 

r 2 


2 ! 


Plain Helical Matched Herringbone Staggered Herring- 
Gear Gear bone Gear 



Relation between Helix 
and Pressure Angles 


Helix Angle “A” 
of Gear Tooth 

Diametral Pitch 

Vl 

% 

Vd 

8 /io 

10 /l2 

12 /l4 

Minimum Width of Face “F” in Inches 

15° 

2.345 

1.954 

1.675 

1.465 

1.172 

0.977 ' 

230 

1.480 

1.233 

1.057 

0.925 

0.740 

0.617 


is equal to twice the width of face of a plain helical gear, plus the 
width of the clearance groove which it is necessary to provide in 
order to have a space for the cutter to run into. By staggering the 
teeth, the total width of face of a herringbone gear can be reduced so 
that it is equal to the width of a plain helical, plus the clearance space. 


Helical Gear Definitions 


As has been previously mentioned, spur helical gears are simply 
ordinary spur gears with the teeth twisted or set at an angle. The 
shafts on which they run are parallel, so that their action is that of a 
true spur gear. It is, therefore, obvious that the definitions given 





























































120 


HELICAL GEAR DEFINITIONS 


for spur gears in Chapter IX also apply to helical gears. The twisting 
of the teeth or the setting of them at an angle, however, changes the 
shape of the tooth, depending upon the plane from which it is viewed. 

This can best be seen by referring to the illustration accompanying 
Table VII. Here the tooth of a parent helical rack is laid out in two 
planes known as the normal and diametral plane. It is clear from 
this illustration that the section of the tooth in the normal plane has 
a different shape from that given by the true section or diametral 
plane. The normal tooth thickness at the pitch line is less than the 
thickness on the true section; this has the effect of making the tooth 
of a finer pitch on the normal section. The normal pitch is, therefore, 
less than the true pitch. 

In calculating the elements of helical gears, two methods can be 
used, namely, calculating on the normal or diametral plane. The 
easiest and simplest way is to calculate the elements, such as the 
tooth thickness, pitch and pressure angle on the diametral plane, and 
when this method is followed, the calculations follow the same rules 
as those given for regular spur gears. 


T* t • rj ( 


CHAPTER XII. 


Tables of Gear Tooth Parts 

The following tables will be found convenient in obtaining the 
various proportions of gear teeth without calculation, and are useful 
for reference purposes. The data in these tables has been obtained 
by the rules and formulas given in Chapters X and XI. 

The conversion tables from the English to the Metric or Module 
system are also included for the benefit of those who have to use both 
systems. 

In addition to conversion tables for gear tooth parts, several 
tables are also included for the conversion of inches to millimeters 
and millimeters to inches. Table XIII gives the equivalents of 
hundredths of millimeters in inches. Table XIV gives the equiva¬ 
lents of inches into millimeters, whereas Table XV gives the equiva¬ 
lents of millimeters in inches, ranging from one millimeter up to and 
including 500 millimeters. In the use of this last table the decimal 
equivalents in inches of 1 to 9 millimeters are given in the top line 
in the body of the table. Then starting with the first column of the 
first line is given the decimal equivalent of 10 millimeters; the 
second column, 11 millimeters; the third column, 12 millimeters, etc. 

In the conversion of millimeters into inches, care should be taken 
in the proper location of the decimal point. For example, let it be 
required to find the decimal equivalent in inches of 240.20 milli¬ 
meters. Referring to Table XV, we will find that 240 millimeters 
equals 9.4490 inches, and by referring to Table XIII, we will find 
that 0.20 millimeters equals 0.0079 inches. Therefore, the decimal 
equivalent of 240.20 = 9.4490+0.0079 = 9.4569 inches. 


122 


GEAR TABLES 


Table VIII.—Gear Tooth Parts 
(Standard 14J^° Involute Tooth Form) 

The Fellows Gear Shaper Co. Standard 


Diame¬ 

tral 

Pitch 

DIMENSIONS IN INCHES 

Thickness on 
Pitch Line 

Addendum 

Dedendum 

Plus 

Clearance 

Whole Depth 
of Tooth 

Double 
Depth 
of Tooth 

4 

0.3927 

0.2500 

i «« . 

0.3125 

0.5625 

1.1250 

5 

0.3142 

0.2000 

0.2500 

0.4500 

0.9000 

6 

0.2618 

0.1666 

0.2083 

0-375° 

0.7500 

7 

0.2244 

0.1429 

0.1786 

0.3215 

0.6430 

8 

0.1963 

0.1250 

0.1562 

0.2812 

0.5624 

9 

0.1745 

0.1II 1 

0.1389 

0.2500 

0.5000 

IO 

0.1571 

0.1000 

0.1250 

0.2250 

0.4500 

ii 

0.1428 

0.0909 

0.1136 

0.2045 

0.4090 

12 

0.1309 

0.0833 

0.1042 

0.1875 

o- 375 o 

13 

0.1208 

0.0769 

0.0961 

0.1730 

0.3460 

14 

0.1122 

0.0714 

0.0893 

0.1607 

0.3214 

*5 

0.1047 

0.0666 

0.0833 

0.1499 

0.2998 

16 

0.0982 

0.0625 

0.0781 

0.1406 

0.2812 

*7 

0.0924 

0.0588 

0.0734 

0.1322 

0.2644 

T8 

0.0873 

0.0555 

0.0695 

0.1250 

0.2500 

*9 

0.0827 

0.0526 

0.0658 

0.1184 

0.2368 

20 

0.0785 

0.0500 

0.0625 

0.1125 

0.2250 

21 

0.0748 

0 0476 

0.0595 

0.1071 

0.2142 

22 

0.07 14 

0.0455 

On 

VO 

O 

d 

0.1024 

0.2048 

23 

0.0683 

0.0434 

0.0543 

0.0977 

0.1954 

24 

0.0654 

0.0417 

0.0521 

0.0938 

0.1876 


















GEAR TABLES 


123 


Table IX.—Gear Tooth Parts 
(20° Pressure Angle, Stub-tooth Form) 

The Fellows Gear Shaper Co. Standard 


Diame¬ 

tral 

Pitch 

DIMENSIONS IN INCHES 

Thickness on 
Pitch Line 

Addendum 

Dedendum 

Plus 

Clearance 

Whole Depth 
of Tooth 

Double 
Depth 
of Tooth 

4/5 

0.3925 

0.2000 

0.2500 

0.4500 

0.9000 

5/7 

0.3140 

0.1429 

0.1785 

0.3214 

0.6428 

6/8 

0.2617 

0.1250 

0.1562 

0.2812 

0.5624 

7/9 

0.2243 

O.IIIO 

0.1389 

0.2500 

0.5000 

8/10 

0.1962 

O.IOOO 

0.1250 

0.2250 

0.4500 

9/11 

0.1744 

0.0909 

0 -H 37 

0.2046 

0.4092 

10/12 

0.1570 

0.0833 

0.1042 

0.1875 

o- 375 o 

11/14 

0.1428 

0.0714 

0.0893 

0.1607 

0.3214 

12/14 

0.1308 

0.0714 

0.0893 

0.1607 

0.3214 

13/16 

0.1208 

0.0625 

0.0781 

0.1406 

0.2812 

14/18 

0.1121 

0 

b 

Co 

CO 

0.0695 

0.1250 

0.2500 

15/20 

0.1047 

0.0500 

0.0625 

0.1125 

0.2250 

16/21 

0.0981 

0.0476 

0.0595 

0.1071 

0.2142 

17/22 

0.0924 

0.0455 

0.0568 

0.1023 

0.2046 

18/24 

0.0872 

0.0417 

0.0520 

0.0937 

0.1874 

19/25 

0.0826 

0.0400 

0.0500 

0.0900 

0.1800 

20/26 

VO 

00 

O 

d 

0.0385 

0.0481 

0.0866 

0.1732 - 

21/28 

0.0748 

0.0357 

0.0446 

0.0803 

0.1606 

22/29 

0.0714 

0.0345 

0.0431 

0.0776 

0.1552 

23/3° 

0.0683 

0-0333 

0.0417 

0.0750 

0.1500 

24/32 

0.0654 

0.0312 

0.0391 

0.0703 

0.1406 


















2 + 


GEAR TABLES—METRIC 


Table X.—Gear Tooth Parts, Module (Metric) System 
(Standard 14^° Involute Tooth Form) 

The Fellows Gear Shaper Co. Standard 


Module 

DIMENSIONS IN INCHES 

Thickness on 
Pitch Line 

Addendum 

Dedendum 

Plus 

Clearance 

Whole Depth 
of Tooth 

Double 
Depth 
of Tooth 

i 

0.0618 

0.0394 

0.0492 

0.0886 

0.1772 

i K 

0.0773 

0.0492 

0.0615 

0.1107 

0.2214 

iK 

0.0927 

0.0591 

0.0739 

0.1330 

0.2660 

iK 

0.1082 

0.0689 

0.0861 

0.1550 

0.3100 

i 

0.1236 

0.0787 

0.0984 

0.1771 

o.3542 

z'A 

0.1391 

0.0885 

0.1106 

0.1991 

0.3982 


0.1544 

0.0984 

0.1230 

0.2214 

0.4428 


0.1700 

0.1082 

0.1352 

0.2434 

0.4868 

3 

0.1855 

0.1181 

0.1476 

0.2657 

°-53 I 4 

3K 

0.2010 

0.1279 

0.1599 

0.2878 

0.5756 

3K 

0.2164 

0.1378 

0.1722 

0.3100 

0.6200 

3H 

0.2319 

0.1476 

0.1845 

0.3321 

0.6642 

4 

0.2473 

°* 1 575 

0.1969 

o .3544 

0.7088 

4/4 

0.2628 

0.1673 

0.2091 

0.3764 

0.7528 

4/4 

0.2783 

0.1772 

0.2215 

0.3987 

0-7974 

4K 

0.2938 

0.1870 

0.2338 

0.4208 

0.8416 

5 

0.3092 

0.1969 

0.2461 

0.4430 

0.8860 

5 ^ 

0.3247 

0.2067 

0.2584 

0.4651 

0.9302 

5 ^ 

0.3401 

0.2166 

0.2707 

0.4873 

0.9746 

5 >< 

o .3556 

0.2264 

0.2830 

0.5094 

1.0188 

6 

0.3710 

0.2362 

0.2952 

0-5 3 J 4 

1.0628 





















GEAR TABLES—METRIC 


125 


Table XI.—Gear Tooth Parts Module (Metric) System 
(20° Pressure Angle, Stub-tooth Form) 

The Fellows Gear Shaper Co. Standard 


Module 

DIMENSIONS IN INCHES 

Thickness on 
Pitch Line 

Addendum 

Dedendum 

Plus 

Clearance 

Whole Depth 
of Tooth 

Double 
Depth 
of Tooth 

2/r .5 

0.1237 

0.0591 

0.0738 

0.1329 

0.2658 

2.25/1.75 

0.1391 

0.0689 

0.0861 

P 

cn 

c/n 

O 

0.3100 

2.5/2 

0.1546 

0.0787 

0.0984 

0.1771 

o .3542 

2.75/2 

0.1700 

0.0787 

0.0984 

0.1771 

o .3542 

3/2- 2 5 

0.1855 

OO 

OO 

O 

d 

0.1106 

0.1991 

0.3982 

3- 2 5/ 2 -5 

0.2010 

0.0984 

0.1230 

0.2214 

0.4428 

3-5/ 2 -5 

0.2164 

0.0984 

0.1230 

0.2214 

0.4428 

3-75/2-75 

0.2319 

0.1082 

0.1352 

0.2434 

0.4868 

4/3 

0.2473 

o.n8i 

0.1476 

0.2657 

0 - 53 U 

4 - 25 / 3-25 

0.2628 

0.1279 

0.1599 

0.2878 

0.5756 

4-5/3- 2 5 

0.2783 

0.1279 

0.1599 

0.2878 

0.5756 

4-75/3-5 

0.2938 

0.1378 

0.1722 

0.3100 

0.6200 

5/3-75 

0.3092 

0.1476 

0.1845 

0.3321 

0.6642 

5- 2 5/4 

0.3247 

0.1575 

0.1969 

0.3544 

0.7088 

5-5/4 

0.3401 

0.1575 

0.1969 

0.3544 

0.7088 

5-75/4-5 

o-355o 

0.1772 

0.2215 

0.3987 

0.7974 

6/4.5 

0.3710 

0.1772 

0.2215 

0.3987 

0.7974 

















126 


GEAR TABLES—CONVERSION 


Table XII.—Circular and Diametral Pitch 
Equivalents of Module Pitches 

The Fellows Gear Shaper Co. Standard 


c 


3 - i 4 i 6 

% 

tch =0.12368 X 

Module 

ircuitir x itcn 

Diametral Pitc 

Diametral I 

. " cuiar 11 

h 

2 5-409 

Module 

Module 

Diametral 

Pitch 

Circular 
Pitch in 
Inches 

1 

Module 

Diametral 

Pitch 

Circular 
Pitch in 
Inches 

A 

i 01.600 

0.031 

3 3 A 

6-775 

0.464 

A 

50.800 

0.062 

4 

6.350 

0.495 

A 

33-867 

0.093 

4 A 

5.978 

0-534 

i 

25.400 

0.124 

4 A 

5.644 

0.556 

*A 

20.320 

0.155 

4 3 A 

5-349 

0.587 

i'A 

16.933 

0.186 

5 

5.080 

0.618 

iA * 

I 4 - 5 X 4 

0.216 

SA 

4.858 

0.649 

2 

12.700 

0.247 

SA 

4.618 

0.680 

2'/i 

11.288 

0.278 

S 3 A 

4.419 

0.711 

2'/ 2 

10.160 

0.309 

6 

4-233 

0.742 

2 A 

9.236 

0.340 

6A 

4.064 

0-773 

3 

8.466 

°-37 1 

6A 

3-9°9 

0.804 

3'A 

7.818 

0.402 

6A 

3-764 

0.835 

3A 

7.257 

o-433 

7 

3.628 

0.866 
























CONVERSION OF MILLIMETERS INTO INCHES 


127 


Table XIII.—Hundredths of Millimeters 
converted into Inches 


Milli¬ 

meters 

Inches 

Milli¬ 

meters 

Inches 

Milli¬ 

meters 

Inches 

Milli¬ 

meters 

Inches 

0.01 

0.0004 

0.26 

0.0102 

0.051 

0.0201 

0.076 

0.0299 

0.02 

0.0008 

0.27 

0.0106 

0.052 

0.0205 

0.077 

0.0303 

0.03 

0.0012 

0.28 

0.0110 

0.053 

0.0209 

0.078 

0.0307 

0.04 

0.0016 

0.29 

0.0114 

0.054 

0.0213 

0.079 

0.0311 

0.05 

0.0020 

0.30 

0.0118 

0.055 

0.0217 

0.080 

0.0315 

0.06 

0.0024 

0.31 

0.0122 

0.056 

0.0220 

0.081 

0.0319 

0.07 

0.0028 

0.32 

0.0126 

0.057 

0.0224 

0.082 

0.0323 

0.08 

0.0031 

o -33 

0.0130 

0.058 

0.0228 

0.083 

0.0327 

0.09 

0.0035 

o .34 

0.0134 

0.059 

0.0232 

0.084 

0.0331. 

O.IO 

0.0039 

0-35 

0.0138 

0.060 

0.0236 

0.085 

0-0335 

O.I I 

0.0043 

0.36 

0.0142 

0.061 

0.0240 

0.086 

0.0339 

O.I2 

0.0047 

0-37 

0.0146 

0.062 

0.0244 

0.087 

0.0343 

0.13 

0.0051 

0.38 

0.0150 

0.063 

0.0248 

> 

0.088 

0.0346 

O.I4 

0.0055 

o .39 

0.0154 

0.064 

0.0252 

0.089 

0.0350 

0.15 

0.0059 

0.40 

0.0157 

0.065 

0.0256 

0.090 

0.0354 

0.16 

0.0063 

0.41 

0.0161 

0.066 

0.026c 

0.091 

0.0358 

0.17 

0.0067 

0.42 

0.0165 

0.067 

0.0264 

0.092 

0.0362 

0.18 

0.0071 

0-43 

0.0169 

0.068 

0.0268 

0.093 

0.0366 

0.19 

0.0075 

0.44 

0.0173 

0.069 

0.0272 

0.094 

0.0370 

0.20 

0.0079 

0.45 

0.0177 

0.070 

0.0276 

0.095 

0.0374 

0.21 

0.0083 

0.46 

0.0181 

0.071 

0.0280 

0.096 

0.0378 

0.22 

0.0087 

0.47 

0.0185 

0.072 

0.0283 

0.097 

0.0382 

O.23 

0.0091 

OO 

d 

0.0189 

0.073 

0.0287 

0.098 

0.0386 

O.24 

0.0094 

0.49 

0.0193 

0.074 

0.0291 

0.099 

0.0390 

O.25 

0.0098 

0.50 

0.0197 

0.075 

0.0295 

0.100 

0.0394 
























128 


CONVERSION OF DECIMALS OF AN INCH INTO MILLIMETERS 


Table XIV.—Decimals of an Inch Converted 
into Millimeters 


Inches 

Milli¬ 

meters 

Inches 

Milli¬ 

meters 

Inches 

Milli¬ 

meters 

Inches 

Milli¬ 

meters 

O.OOI 

0.025 

0.200 

5.08 

O.480 

12.19 

0.760 

19.30 

0.002 

0.051 

0.210 

5-33 

0.490 

i 

12.45 

0.770 

19.56 

O.OO3 

0.076 

0.220 

5-59 

0.500 

12.70 

0.780 

19.81 

O.OO4 

0.102 

0.230 

5.84 

0.510 

12.95 

0.790 

20.07 

O.OO5 

0.127 

0.240 

6.10 

0.520 

13.21 

0.800 

20.32 

0.006 

0.152 

0.250 

6-35 

0.530 

13.46 

0.810 

20.57 

0.007 

0.178 

0.260 

6.60 

0.540 

13.72 

0.820 

20.83 

0.008 

0.203 

0.270 

6.86 

I 

0.550 

13-97 

0.830 

21.08 

O.OO9 

0.229 

0.280 

7.11 

0.560 

14.22 

0.840. 

21-34 

0.010 

0.254 

0.290 

7-37 

0-570 

14.48 

0.850 

21.59 

0.020 

0.508 

0.300 

7.62 

0.580 

14-73 

0.860 

21.84 

O.O3O 

0.762 

0.310 

7.87 

0.590 

14.99 

0.870 

22.10 

O.O4O 

1.016 

0.320 

8.13 

0.600 

15.24 

0.880 

22.35 

0.050 

1.270 

0.330 

8.38 

0.610 

15.49 

0.890 

22.61 

O.060 

1.524 

0.340 

8.64 

0.620 

15-75 

0.900 

22.86 

0.070 

1.778 

0.350 

8.89 

0.630 

16.00 

0.910 

23.11 

0.080 

2.032 

0.360 

9.14 

0.640 

16.26 

0.920 

23.37 

O.O9O 

2.286 

0.370 

9.40 

0.650 

16.51 

0.930 

23.62 

0.100 

2.540 

0.380 

9.65 

0.660 

16.76 

0.940 

23.88 

O.IIO 

2.794 

0.390 

9.91 

0.670 

17.02 

0.950 

24-13 

0.120 

3.048 

0.400 

10.16 

0.680 

17.27 

0.960 

24.38 

0.130 

3-302 

0.410 

10.41 

0.690 

17-53 

0.970 

24.64 

0.140 

3-56 

0.420 

10.67 

0.700 

17.78 

0.980 

24.89 

O.I5O 

3.81 

0.430 

10.92 

0.710 

18.03 

0.990 

25.15 

O.160 

4.06 

0.440 

11.18 

0.720 

18.29 

1.000 

25.40 

O.I70 

4-32 

0.450 

H -43 

0.730 

18.54 



0.180 

4-57 

0.460 

11.68 

0.740 

18.80 



O.I9O 

4-83 

0.470 

11.94 

0.750 

19.05 























CONVERSION OF MILLIMETERS INTO INCHES 


129 


Table XV.—Conversion of Millimeters into Inches 


MILLIMETERS 

Milli- 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

meters 

Decimal Equivalents in Inches 



0.0394 

0.0787 

0.1181 

0.1575 

0.1969 

0,2362 

0.2756 

0.3150 

0.3543 

10 

0.3937 

0.4331 

0.4724 

0.5118 

0.5512 

0.5906 

0.6299 

0.6693 

0.7087 

0.7480 

20 

0.7874 

0.8268 

0.8662 

0.9055 

0.9499 

0.9843 

1.0236 

1.0630 

1.1024 

1.1418 

30 

1.1811 

1.2205 

1.2599 

1.2992 

1.3386 

1.3780 

1.4173 

1.4567 

1.4961 

1.5355 

40 

1.5748 

1.6142 

1.6536 

1.6929 

1.7323 

1.7717 

1.8111 

1.8504 

1.8898 

1.9292 

50 

1.9685 

2.0079 

2.0473 

2.0867 

2.1260 

2.1654 

2.2048 

2.2441 

2.2835 

2.3229 

60 

2.3622 

2.4016 

2.4410 

2.4804 

2.5197 

2.5591 

2.5985 

2.6378 

2.6772 

2.7166 

70 

2.7560 

2.7953 

2.8347 

2.8741 

2.9134 

2.9528 

2.9922 

3.0316 

3.0709 

3.1103 

80 

3.1497 

3.1890 

3.2284 

3.2678 

3.3071 

3.3465 

3.3859 

3.4253 

3.4646 

3.5040 

90 

3.5434 

3.5827 

3.6221 

3.6615 

3.7009 

3.7402 

3.7796 

3.8190 

3.8583 

3.8977 

100 

3.9371 

3.9764 

4.0158 

4.0552 

4.0946 

4.1339 

4.1733 

4.2127 

4.2520 

4.2914 

110 

4.3308 

4.3702 

4.4095 

4.4489 

4.4883 

4.5276 

4.5670 

4.6064 

4.6458 

4.6851 

120 

4.7245 

4.7639 

4.8032 

4.8426 

4.8820 

4.9213 

4.9607 

5.0000 

5.0394 

5.0788 

130 

5.1182 

5.1576 

5.1969 

5.2363 

5.2757 

5.3151 

5.3544 

5.3938 

5.4332 

5.4725 

140 

5.5119 

5.5513 

5.5907 

5.6300 

5.6694 

5.7088 

5.7481 

5.7875 

5.8269 

5.8662 

150 

5.9056 

5.9450 

5.9844 

6.0237 

6.0631 

6.1025 

6.1418 

6.1812 

6.2206 

6.2600 

160 

6.2993 

6.3387 

6.3781 

6.4174 

6.4568 

6.4962 

6.5356 

6.5749 

6.6143 

6.6537 

170 

6.6930 

6.7324 

6.7718 

6.8111 

6.8505 

6.8899 

6.9293 

6.9686 

7.0080 

7.0474 

180 

7.0867 

7.1261 

7.1655 

7.2049 

7.2442 

7.2836 

7.3230 

7.3623 

7.4017 

7.4411 

190 

7.4805 

7.5198 

7.5592 

7.5986 

7.6379 

7.6773 

7.7167 

7.7560 

7.7954 

7.8348 

200 

7.8742 

7.9135 

7.9529 

7.9923 

8.0316 

8.0710 

8.1104 

8.1498 

8.1891 

8.2285 

210 

8.2679 

8.3072 

8.3466 

8.3860 

8.4253 

8.4647 

8.5041 

8.5435 

8.5828 

8.6222 

220 

8.6616 

8.7009 

8.7403 

8.7797 

8.8191 

8.8584 

8.8978 

8.9372 

8.9765 

9.0159 

230 

9.0553 

9.0947 

9.1340 

9.1734 

9.2128 

9.2521 

9.2915 

9.3309 

9.3702 

9.4096 

240 

9.4490 

9.4884 

9.5277 

9.5671 

9.6065 

9.6458 

9.6852 

9.7246 

9.7640 

9.8033 

250 

9.8427 

9.8820 

9.9214 

9.9608 

10.0000 

10.0395 

10.0789 

10.1182 

10.1576 

10.1970 

260 

10.2364 

10.2757 

10.3151 

10.3545 

10.3938 

10.4332 

10.4726 

10.5119 

10.5513 

10.5907 

270 

10.6301 

10.6694 

10.7088 

10.7482 

10.7875 

10.8269 

10.8663 

10.9057 

10.9450 

10.9844 

280 

11.0238 

11.0331 

11.1025 

11.1419 

11.1813 

11.2206 

11.2600 

11.2994 

11.3387 

11.3781 

290 

11.4175 

11.4568 

11.4982 

11.5356 

11.5750 

11.6143 

11.6537 

11.6931 

11.7324 

11.7718 

300 

11.8112 

11.8506 

11.8899 

11.9293 

11.9887 

12.0080 

12.0474 

12.0868 

12.1261 

12.1655 

310 

12.2049 

12.2443 

12.2836 

12.3230 

12.3624 

12.4017 

12.4411 

12.4805 

12.5199 

12.5592 

320 

12.5986 

12.6380 

12.6773 

12.7167 

12.7561 

12.7955 

12.8348 

12.8742 

12.9136 

12.9529 

330 

12.9923 

13.0317 

13.0711 

13.1104 

13.1498 

13.1892 

13.2285 

13.2679 

13.3073 

13.3466 

340 

13.3860 

13.4254 

13.4648 

13.5041 

13.5435 

13.5829 

13.6222 

13.6616 

13.7010 

13.7403 

350 

13.7797 

13.8191 

13.8585 

13.8978 

13.9372 

13.9766 

14.0159 

14.0553 

14.0947 

14.1341 

360 

14.1734 

14.2128 

14.2522 

14.2915 

14.3309 

14.3703 

14.4097 

14.4490 

14.4884 

14.5278 

370 

14.5671 

14.6035 

14.6459 

14.6851 

14.7246 

14.7640 

14.8034 

14.8427 

14.8821 

14.9215 

380 

14.9808 

15.0002 

15.0396 

15.0790 

15.1183 

15.1577 

15.1971 

15.2364 

15.2758 

15.3152 

390 

15.3546 

15.3939 

15.4333 

15.4727 

15.5120 

15.5514 

15.5908 

15.6301 

15.6695 

15.7089 

400 

15.7483 

15.7876 

15.8270 

15.8664 

15.0057 

15.9451 

15.9845 

16.0238 

16.0632 

16.1026 

410 

16.1420 

16.1813 

16.2207 

16.2601 

16.2994 

16.3388 

16.3782 

16.4176 

16.4569 

16.4963 

420 

16.5357 

16.5751 

16.6144 

16.6538 

16.6932 

16.7325 

16.7719 

16.8113 

16.8506 

16.8900 

430 

16.9294 

16.9888 

17.0081 

17.0475 

17.0869 

17.1262 

17.1656 

17.2050 

17.2443 

17.2837 

440 

17.3231 

17.3625 

17.4018 

17.4412 

17.4806 

17.5199 

17.5593 

17.5987 

17.6381 

17.6774 

450 

17.7168 

17.7562 

17.7955 

17.8349 

17.8743 

17.9137 

17.9530 

17.9924 

18.0318 

18.0711 

460 

18.1105 

18.1499 

18.1893 

18.2286 

18.2679 

18.3073 

18.3467 

18.3861 

18.4253 

18.4648 

470 

18.5042 

18.5436 

18.5830 

18.6223 

18.6617 

18.7011 

18.7404 

18.7798 

18.8192 

18.8586 

480 

18.8979 

18.9373 

18.9767 

19.0160 

19.0554 

19.0948 

19.1341 

19.1735 

19.2129 

19.2523 

490 

19.2916 

19.3310 

19.3704 

19.4097 

19.4491 

19.4885 

19.5279 

19.5672 

19.6066 

19.6460 

500 

19.6853 






































Table XVI.—Conversion of Fractions of an Inch into Millimeters 


INCHES INTO MILLIMETERS 


130 



o 


O 




no 


NO 


■+ 



Ct 


rt-wco m no d on NO n Q no ro O F ■+ >-> 00 ~t — 00 no ct on no co on no <0 O F 

CT\ C?N 00 00 00 F F FNO no no no nononoF-F-F-cocococi d d >- -h I-. O O O O On 

i— 1 —* no o co f -< no o co f ci no o co f m no on co r- « ^o\<obH no o co f o 


F" no no nono NO F F Fco 00 OnOnOnO O m <-> <-> d d co co co F" F - no no no no no f 
OOOOOOOOOOOOOO^'-"”^^-^" — h-^-hhhhhhi-i^i-.m 

cocococococococococococococococococococococococococococococococo 


-t- co no d On NO co ON no coO F F- "i m m Nod On no d On no co O t^coO F 

ON On oo go 00 F F FnO nOndnO ^Noin + 'fl-cococod d d 1-1 — hh o O O On 

(OfN M NO ON CO tN H NoO\COtNM NOC\COt^H NO ON O M ^ ON O « NoON CONO 


OOO O O o "i d d d co co + -t no nono nono |n Foo ooMOnOnOOOhh 
r- r-CO OOOOOOOOOOOOOOOOOOOOOOOOOOCOOOCOCOOOOOOOOOOOCOOO OnOnOnONON 
dddddddddddddddddddddddddddddddd 


no d ON no d On NO co O F F- O N i- m 00 Nod ON no d ON NO coO t^coO ■+ m co 

on on 00 00 00 f f fno nono ^lo^ + ^itcocood d d d — ►- ~c o o o on 

On co m NO On CO r^- -I no (j\ cot^H no O co F ^ ON to t^M nocncoi^h no On d 


CO + + NO NO NONO NO F F Foo 00 OnOnOnO O — >-* >-< d d co CO co -t + NO NO nono 
iy~, no no no no no no No no no no no no no no no NO no NO no no no no no no no no NO no NO no no 
dddddddddddddddddddddddddddddddd 


no d Os no co O tN o O In ■+ h 00 no d x Nod ONO d OnO <0 O F F- 00 no — 00 

on on co co 00 00 f f fno nono u-i nt, no + -t -t o o o o ct d d -> >- « o O O On 

no O co F i-i no o (n « >ci 0 NCOInm ^lONC^hM >oONCorNH nooo 


oo 00 O O O O O <-* «-■ d d d <0 co F" F- F- no nono nono f Foo 00 00 cnonO O O 
d d d d roco'ococococococococoforocofotocococococococococo'l-'j-'t 
dddddddddddddddddddddddddddddddd 


NO COONO COO d i- O 00 + HX Nod ON NO CO ON NO CO O d + M X + H X Nod ON 

ON ON Onoo x m (n [n r^NO NONO no no no F" F - -t O X O co d d d >-> >-i « O O O ON 

«-■ No ON CO H no O co F ci NO ON co d w noOncoinm noONONh no On CO « F- 


co co co -t no no nono no Foo 00 OnOnOnO O « i-c «-idd co co co i- ■+ no no 

OOOOOOOOOOOOOOOOOO i - ,i -''-''-'>-ii-'i-''-|'-|'-i — — « •-> 

dddddddddddddddddddddddddddddddd 


r^coO F F" In + « « Nod On no d On no coO F F- ~ F- ~ 00 Nod On no d On 
On ON Onoo 00 00 r-' I"- FnC nono Noir,Nr,-t-t-t-toocodd d ~ -h m o O O On 
r—• <—1 no on co m no on co I s - « on n I s - « n-, cn co ^ on co r 'm no on co o 

r^OO COCO ON ON O O O — **d Ct d CO CO -t + + NO NONO NONO In FOO CO 00 ON ON O 
r- foo ooooooooooooooooooocoooooooooooooooooooooooooooo on 


-t o 00 + Nod On no d OnnO co O I^coO F" — co no ct co Nod OnnO co 

On On Onoo x m fno no no no no no no F- F - F- co co <0 ct ct ct « — i-« O O O 

co F ci NO ON CO H to On co f' h no On co >- to On co N m no O co F i— no On co F' 

d d co co co i- -t no tc nono nc h h Foo 00 OnOnOnO O 1-1 >-> i-idd co co co -t *t 

NO NO No No NO NO NO No NO NO NO NO No NO NO No NO NO No NONO NO 'O NO NO NO NO NO NO 'O NO NO 


00 r(- h x no ct co Nod OnnO n OnO <o O F- m x no ~ co Nod OnnO co OnnO 

On Os onoo xm Mn fno nonono ‘o'cnc-j- t)- Tj-oond d d <-< « M O O O 

ON co w >cn Q\ co 1 ^ h no On co " no on co m no co h m >c c\ co 1 ^ « no On d 


*8 


NO 

d 


r^co 00 00 
d d d d d 


ONOsO O O m — d d d co co F- F" F- no nono no no F Foo 00 00 O' 
ct d cocococococococococococococococococococococococo 


00 no -• 00 no d OnnO co OnnO co O I F - — OO F" c* 00 Nod ONNO ct OiNO co O F F" M 

ON On Onoo 00 00 F F FnC NONONO Nc,NoNo + -t- + cococod d d d « — _■ O O O 

no ON co w no ON co — nc ON co C'm NoONtObc no On co F no On co F i-- no O 


*-h t —1 d 

OOO 


d 

O 


co co co 

OOO 


F* 

o 


+ No NO No NO NO 

OOOOOO 


f f r^-oo 00 

OOOOO 


0 \ 0 \ 0 \ 00 "«« 

OOO 1- ' 


ct ct CO CO X 


no ct- co ct o 000 no no f- d « o o r -no no co d — 000 r' no co — o o r-NO nc 

00 no d ONO d OnO O O F F" ~ F' + - X Nod O nc, ct OnO co O htO F- >- 
OOO 000000 r^- F Fno NONO no no no f- F- -t ro co co d d d d 1-1 — >-1 O O O 

w noOC^Fh >c O H F h noOCOF^i-i ‘c CN co F h no O CO F - noOCOFh nc 


NO NO NO F FOO OO QO O O O O O l — 1 Ct ct ct co co nc, no NO NO no F Foo 00 

f^oo xxxxxxxxxxxxxxxxxxxxx 


o OX NO Nc, ct « O XI F^nO + Od o OX ND No -F co — O O I^nO nc, co d — <J 

O no d ONO co O F + O f^*F«oo no ct co Nod OnO co O F O O F^cF — oo no« 

O O OOO xxx FF F'NO nono NoicicFtl'COfOCOfOd ct ct « ch O O O 

F- 1-1 no O CO F w >o OCOF « tiO(OF« no O co F^ | —■ no O co F ' 'cCiCOFh 


QwMMCtdOcocoF'F^No nonO no FF F~oo oooOOOO>-'-''-'dctc' 
1 _OIOIONONONONONC, NONONONCINONONONONONONONONONONC, NONO no NO NO NO no NO NO 


no F ct « 

O OO FNO 

F co ct 

O OX NO No 

t Cl H ( 

) CO 

FnO 

F cod 

O 

Ooo 

F- 

no F 

ONO co 0 

F co O F 

•F- i-i 09 

NO M X wo ct 

ONO co C 

5 no 

co 0 


OO 

rt- HH 

OO 

No d 


OOO 000 XX FF F'NO NONO no no no -F -t "F + O CO co ct d d « >1 m O O O 
OFh no O co F « no O co F no O CO F noOcoF*-i noOcoFi-i no O co F 


No NONO NO NO F FOO OOOO OOO O O i-t M d d d co CO -t- ~f- NO nono NO NO F 

d d d d d d d d d d d d ncococococococococococococococoococo 


• 00 FnO *F CO ct O OXNO no 'F ct <-1 O x FnO F O cl O OX NO no *F ct 1-1 O O 

•NO co O F'-cF'—oo *F « 00 Nod ONO co OnO co O F F h f F w X Nod ONO d 

• O O Ooo 00 00 F F FnO nono no no no FFFFFtOFrl d d >-> « ,-c O O O 

• coF>—1 noOCOFm noOcoFi-< no O co F noOcof>-< no O co F no O 


.QOMHHddcococoF'F'do nono no F F F00.00 OOOOO 


d 
















































Table XVII.—Conversion of Fractions of an Inch into Millimeters—Continued 


INCHES INTO MILLIMETERS 


1 3 I 



cm 


3" T ,-£! c 2 ? T 1 r? rt ON'*© n o M-hm nt, hh x nt, d On nt, d qnnO COO h 

Os ON CO OO OO r- r- r- NO NO NO NO Vy~> Vr> t|- ~4- C^} CC N H N 1 -It—■ i-h O O O O C5\ 

’too d NO o t’CO Cl NO o OO cl NO o t’CO d NO O ctCO Cl NO o TfOOrlNO O Tt r- 




mx oo onononO O hh « *-■ cm d n n fn ^ u-,no no Nh mx x on on on 

cococococococococococo<OCococococococococncocococM J cococ')COCOCOCo 


HH 


T T 22 ^ <* On>-ocI On no «00 M <0 O M 7* ■— oo VN O oo nt, d ON no no Nno 

On On OO CO X M M MNO NO NO NO NoNriNriT-rf-Tj-cOCOCOd d d i-i hh hh m O O O 

O 7-x CM NO O 7-00 d NO O Tf-OO CM NO O 7"X (M NO O 7"X CM NO O 7-X CM NO O 

M 

On 

CO 


1—1 


SL ST Si ^ ^ ^ '-h -t- Nr, NO NO NO M MX COM OcONO O 0 H H fC cc fi C-) n ^ + 

OnOnOnOnONONOnOnOnONONONOnOnOnOnOnOnOnOnO O 0 O O O O O O O O O 

CM CM CM Cl CM CM CM CM CM CM CM CM CM <M Ct CM CM CM CM CM COCOCOCOCOCOCOfOfOCOCOCO 


o 


Nr, CM OO Nr, d ON NO cn ONO COO 1^ n)- H OO Nr, hh x Nr, d On NO cn O NO cn o Ni-H 

On OnOO OO OO M M M MNO NO NO Nr, Ir, Nr, t}- -7 nf CO CO CO ddddHHHHHnOOO 

NO O 7-X CM NO O 7-CO Cl NO O 7-00 CM NO O 7"X CM NO O 7*X CM NO O 7"X CM NO 

X 

ON 

ON 




^ F'" F" F^OO OO 0\ 0\ 0\ o O >—< hh w d cl CO C*) CO rt* rf- Vr> ^ Vy^VsQ \Q !"•>» CO CO 0 O 

so^so^o^ovo^o^o r^r^r^t^i^r^r-r^r^i'-r^F : -r^F^r^r^r^r^r^r-r-r-r- 
dcidcicidcicicicicidcicidcicicicscicicicicicidcicicicicici 


ON 


Nr, CM ON NO CO ON NO CO O NOhM t)- h X Nr, d On NO CM ON NO CO O M 7" hh [^ 7 " hh 

ON ONOO OO CO I'' M M MNO NO NO Nr,vr,Nr,T)-T}-rt-COCOCOCM CM Cl CM i-i hh hh O O O 

CM NO O 7-CO CM NO O 7-00 CM NO O 7X CM NO O 7"X CM NO O 7-X CM NO O 7"X CM 

00 

CN 

Vr 



H< CM CM CM CO CO 7* 7- 7- Nr, Nr,NO NO NO (n MX OOXONONOOOwHCMdcMO 

Vr> V-O Vy-'j Vy^j Vy^ Vr> Vy~i ly^ ^ 

dddcicicicicicicidcicicici^dcicicicicicicicicidcicicici 

Vr^ 

cl 


X 


NO CM On NO COO M 7" hh (n ■+ h X Nr, Cl ON Nr, cM ON NO COO M 7" O •+ w X Nr, cl 

ON ONX X X X Mn MNO NO NO Nr, Nr, Nr, 7 - rj- tJ- CO COCO COCMcMcM«r--,000 
OO d NO O i-X CM NO O T - X CM NO O 7" X d NO O 'tx CM NO O 7" X d NO O 7-x 

CO 

ON 



Nr, no no mmmxx on on o, O O « <-> ** cm cm co co co 7 - 7 - nt, vt,no no m m mx 

H M H —, M r* —, — H m cl CM cl CM Cl CM Cl Cl CM CM Cl CM Cl CM Cl Cl Cl Cl Cl Cl Cl 

CMCMCICMCMCMCMCICICMCICMCICMCMCMCMCMCMCMCMCMCMCMCICMCMCMCMCMCMCI 



CO 

J-. 

CD 

4-» 

<D 

C 

NO COO M- O |N+M» Nr, cm X Nr, cM ON NO COO N CO O h X Nr, m X Nr, cl ON 

ON ON ONOO CO CO M M [''NO NO NO Nr,Nr,Nr,-t-rf-^rt-c0COCOCM CM CM hh hh hh O O O ON 

•too cm no O ^-oo cl no O ^-oo cm no O ^too cm no O -t-oo CM NO O ^OO Cl NO O cf- 

X 

0 / 

c 


O O H H cl d Cl r0fO + i-+Nr, Nr,NO NO NO r'' r^CO XXOiONOOOhhcICM 
OnONOnOnONONONONONONONONOnONONOnONONONOnONONONOnO o o o o o o 

,-,,_,,_i-< l _c_,_,_,,_i_ l _i__i_i l _i l _i_>»*,_,r-i l _i,-i,_i_iCMCMCMcMClCMcM 

C4 

0 

cl 

CJ 

c 

NO 

*-h 

fo O f^cj-rHCO Nr, h CO Nr, cl ON NO O O NO CO O [N tJ- m X -f- « CO Nr, CM ON NO CO 

ON ON ONOO X X [N|N r^-NO NO NO Nr, Nr, Nr, Nr, rf- r^- rj- CO CO CO CM CM CM r-c r-, i-i O O O 

O Tj-oo CM NO O -+-CO CM NO O ct-OO CM NO O -f-QO Cl NO O ^"OO CM NO O cf-QO CM NO O 

ON 

ON 

X, 



Nr, Nr, Nr, NO NO f'' CO OO ONONONO O « m m CM Cl CO n fO Nr, Nr, Nr, NO NO 1^ t^ 

nononcnonononononononondno [~^ [^ r'' r'' r^- 

*■^<^*-^1—l»—II—ll-HI—II—iHHI-HI-HI—II—( 


to 


+ M X Tf-MOO Nr, CM ONO CO ON NO CO O h t « X Nr, cl ON NO CM ON NO CO 

ON(0\CF\COCOOO f'' ['' r^-NO NO NO Nr,Nr,Nr,Nr,Tf-Tj-Tj-COCOCOCM CM CM ** m hi O 0 O 
NO O -^-CO Cl NO O ^foo CM NO O *tCO CM NO O ^co CM NO O ^OO CM NO O ^OO CM NO 

§ 



UlOOOHHCMCMCMCOfO+'t'tNr, Nr, NO NO NO S (''OO XXONUOOOmh 
CO , 4" T i"r^-Tf-T}-rt-'^-'^-- r t-Tt-H}-'<^-Tt-Tt-T^-Tt-Tj-'^-rJ-'r)-Ht- T J--^-Tj-Ht-Nr,Nr,Nr,Nr,Nr, 

<►“11—ll-HI—II—II—II—II—II—II—II—l|—II—II—ll-HI—»►—1*—Ml—Ml—MHHl—Ml— 

c< 

vr> 

l-H 




C tn ON nt, cM ON Nr, cl ON^O OOC + OM-hX^CM ONNCCM on no COO MOO 
ON ON CNOO CO OO M M MNO NONONO Nr,Nr,Nr,Tf.T*-Tt-cocococl d d hh h. hh hh O O 0 

cl no O ^foo d no O -f-co d no O -^-oo d no O cf-co d no O ^foo d no O rf-oo d no 


7- 


Th tJ- Nr, Nr, Nr, NO NO M M M OO OO ONONONO O hh hh hh d Cl CO CO CO ’M" ^1* Nr, Nr, »,NO NO 
HHHHHHHHHHHHHHHHHHHHHHHHHHHiHHddCMdCMClddddddd ddCMd 

1 —II—< 1 —II—II—II—II—ll-HI—l»—ll-HI—II—||—II—II—ll-HI—|l—II—II—■!—IHHI—II—ll-SI-HI-HI—IHHI— 11 -H 


CO 


CO CM HH ONOO M Nr, Hf- CO hh O ONOO NO Nr, CO CM hh ONOO MNC "t C) CM O , 

OO Nr, d OO Nr, d On NO COO CCOO r^H 4 -H -00 IT, H ONNr,d ON NO CO O NO CO 7? 

ON ON ON ONOO CO 7" t-' r'' MNO NO NO Nr,Nr,ir,'-t-H}- T }-c0C0C0d d CM d hh hh ~ nM NM 

00 CM NO O 7-00 CM NO O 7-00 d NO O 7-00 CM NO O 7-00 CM NO O 7-00 d NO '-J T. 

.201 I 




ooONONOOOHwdddcocoTrT-T-Nr, ncno no no M Moo x oo on On 9 S Q 
XXX ONONOnONONONONCNONONOnONONOnONOvONONONO,ONONOnONON^ nM NM 

IOI 


cm 


X r"r, Tf n -H o O' N f — NO Nr, CO CM HH ON OO M Nr, Tf CO CM O ON MNO Nr, d) d hh O OO M 

X Nr, CM ON NO CO O NO CO O M 7 - —' X 7" — X Nr,d ON NO CO ON NO n O h -t " x 7 -hh 

OnOnOnxxxx MM Mno ncno Nr,N,ic7Nj-+nnnd d d d H- h- hh q O o 

7-x d no O T-oo d no O 7-oo d no O 7-oo d no O 7 -oo d no O 7-oo d no O 7-x 



CO CO 7 - 7- Nr, Nr, NCNO NO MMMXX ONONONO O hh hh hh CM d n O O -f 7 - Nr, Nr, Nr, 
nOnOnOnOnOnOnOnONONOnOnCnOnCnOnOnO MMMMMMMMMMMMMMM 


HH 


CO hh 0 ON MNO Nr, CO d HH OnX M nc 7 O " O <7, MNO Nr, CO d hh ONX MNO 7- co hh 

On Nr, CO ON NO COO MT-hh [n 7 — X Nr,d ON NO CM ON NO COO M 7 - O MT-hhX Nr, cm 

On On Onx x x x M M mno nOnc >ciri l c777fOCOOcocM d d hh hh hh 0 O O 

O T-oo d no-O T-oo d NO O 7-x d no O T-oo d no O 7-x> d NO O 7-x> cm no O 7- 




XXX ONONO O O hh hh d Cl CM co CO 7 7 7 Nr, Nr, NO NO NO M MX XX ON ON O O 
cococococo7"7"7-7"7"7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7"7-7-7"Nr,N'-, 




1 —NO 7 cod hh ONX M Nr, 7 to h 0 On MnO Nr,cod hh Onx M nt, 7 - ro hh 0 Os MNO 

ON NO COO MT-O M 7- Hi X Nr, CM ONNcd ON NO O O M CO O M7-hhX nt, CM X Nr, d 

ON ON ON ONX X X MM MNO NO NO Nr,ir,Nr,7777corood d d HH HH HH 0 O 0 

sO O T-oo d NO O 7-x d no O 7-x cm no O 7-oo cm no O 7-co d no O 7-co <7 no O 




CM co CO CO 7 7 Nr, Nr, Nr, NO NO MMMXX On ON On O O hh hh hh d d co co O 7 7vr, 

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH'HHHHHHdddddddClddddd 

Inch 

r-i\ rcj^O»— i|co ^Jr— 1 »— (|cc c*o|<Cio\'^|«OCs!c y : »o|<OH*h<©!<C«| c5ifi|<0 
















































13-2 


DECIMAL EQUIVALENTS OF INCHES 


Table XVIII.—Decimal Equivalents of an Inch 


.015625 

T2.03125 

.O46875 

A.06250 

.078125 


515625 

53125 

546875 

5625 O 

578125 


3 

32. 

7 

64. 

H 

9 

64. 

5 

32. 

11 

64. 

3 

16 • • • 
13 

64 ...... . 

7 

32. 


15 

4 


17 . 

4 


9 

32 


11 

4 


-16 


X 


IX 

32 


23 

64 • 


2 5 

64 


H 


13. 


2.1 

4 





31 

64 




.09375 

.109375 

.12500 

.140625 

.15625 

.171875 

.18750 

.203125 

.21875 

•234375 

.25000 

.265625 

.28125 

.296875 

.31250 

.328125 

•34375 

•359375 

•37500 

.390625 

.40625 

.421875 

.43750 

•453125 

.46875 

•484375 

.50000 


19 

32 


39 

64 


S A 


41 

64 • • 

21 

32 

43 

64 ■ • 


1 1 
16 


45 

64 


23 

32 


47 

64 


49 

64 


25 

3 2' - • 

51 

64 ... . 

1 3 
16 


53 
"6 4 


X 


2 7. 


3 2 


55 

64 



29 

32 


51 
64 • 


1 5 
16 


61 
6 4 


31 


3T 


63 

64 


•59375 

.609375 

.62500 

.640625 

.65625 

.671875 

.68750 

.703125 

.71875 

•734375 

.75000 

.765625 

.78125 

.796875 

.81250 

.828125 

•84375 

•859375 

.87500 

.890625 

.90625 

•921875 

•93750 

•953125 

.96875 

•984375 

1.00000 





































































INDEX 


Action, line of, 107 

Addendum, corrected, rules for, 108, 109, 
110 

rules for calculating, 104 
Aluminum, cooling compounds for, 87 
Alloy steel, cutting oils for, 86 
Angle, necessity for obtaining correct 
helix, 36 

of obliquity, rule for calculating, 107 
Apron, adjusting of location block for 
5 2 > 53,. 54. 

lever, adjusting tension on, 49, 50, 51, 

5 2 

Arbor, clamping work on, 15 
Gear Shaper, 63 

necessity for hardening and grinding, 
66, 67 

removing from spindle, 13 
testing concentricity of, 9, 13 
selection of, 12 

Automobile transmission gears, methods 
of holding, 67, 69, 70, 74 


Back gears, setting of, 15, 16, 17, 19 
Backing off, eccentric roll, adjusting of, 
5°,.5 I 

Base circle diameter, external gears, 
rules for calculating, 107 
internal gears, 113 

Bearing, adjusting of lower on No. 6 
Gear Shaper, 45, 46 
adjusting on No. 65 Helical Gear 
Shaper, 46, 47 

Bell-ringer, setting of, 26, 28 
Brass, cooling compounds for, 87 
Bronze, cooling compounds for, 87 


Cast iron, cooling compounds for, 85 
Center distances, measuring of, 90, 91 
rules for calculating, 103, 112 
tolerances for, 89 

Change gears, example of calculating, 93, 
94 

formula for calculating, 93 
selecting, 9 
setting of, 14, 18 
table of, 6 

Chart, table of change gears, 6 


Chordal tooth thickness, rule for calcu¬ 
lating, 108, 109 
table of, 100 

Circular pitch, formula for calculating, 
101 

Clearance of gears cut on the Gear 
Shaper, 104 

rules for calculating, 104 
Cloth, cutting of, 87 

Clutch disks, methods of holding, 68, 69, 

7° 

holding driving drum for, 82 
Cluster gears, methods of holding, 74, 75 
Common tangent, definition of, 107 
Concentricity of gears, 88 
methods of testing, 89, 90, 91 
tolerances for, 15 

Cooling compounds for cutter sharpen¬ 
ing, 62 

for gear cutting, 85 
Counterbalance spring, use of, 23 
Cross-rail, adjusting saddle-gib on, 48 
Cutter, adjusting for position relative to 
gear blanks, 23 

centering with gear blank, 23, 26 
charts showing relation of cutter to 
gear blanks, 21 

cooling compounds for sharpening, 62 
method of mounting for “pull” and 
“push” strokes, 4, 5, 24 
Cutter, method of setting helical, 25 
selecting and mounting, 4, 7 
setting to gear blanks for stroke, 21, 22 
setting to a master gear, 29, 30 
setting in relation to blank for depth 
of cut, 28, 29 

sharpening helical, 58, 59, 60, 61 
sharpening spur, 57, 58, 59 
Cutter-guide, adjusting of taper gib on 
No. 6 Gear Shaper, 42 
Cutter-spindle bearing, adjusting of 
lower on No. 6 Gear Shaper, 45, 46 
adjusting of lower on helical Gear 
Shaper, 46 

Cutting speeds, selection of, 20 


Depth of tooth, rules for calculating, 104 
Dial-nut, adjusting of, 48, 49, 51 

pitch, setting of for depth of cut, 24, 27 
Diameter, root, rules for calculating, 106 


134 


DIAMETRAL PITCH—GEAR SHAPER 


Diametral pitch, 102 
definition of, 102 
rules for calculating, 102 
Directions for setting-up and operation 
of Gear Shaper, 3-34 
Disk clutch, method of holding driving 
drum, 82 

Disks, methods of holding friction clutch, 

69 

Double-cut mechanism, setting of, 27, 28 

Faceplate and work-supports, 63, 68 
Feeds for cutter sharpening, 61, 62 
for Gear Shaper, 6 
Fiber, cutting of, 87 
Formulas and rules, 93-120 

Gaging and inspecting gears, 88-92 
important points on, 92 
Gear, example to cut, 3, 7 
Gear blanks, faces should be true with 
holes, 66 
holding, 67, 68 

universal fixture for internal gears, 83 
important points on holding and clamp¬ 
ing, 84 

points on clamping, 84 

resetting for recutting, 37, 38 

rules for calculating outside diameter, 

J ? 5 ... 

testing concentricity of, 10, 12, 13 

Gear Cutting, oils and cooling com¬ 
pounds for, 85 

Gear rings, method of holding internal, 80 
Gear teeth, chordal thickness, table of, 
100 

conversion of circular to diametral 
pitch, 102 

diagram giving notation of internal, 112 
of spu r , 99 
forms, of, 97 

instructions for calculating elements 
of, 98 

names of various elements of spur, 99 
pressure angle standard involute, 97 
20° stub-tooth form, 97 
proportions for standard involute, 98, 
122, 124 

2o° stub-tooth form,"123, 125 
roughing and finishing, summary of, 
important points on, 40 
rules for calculating elements of, 97-120 
tables of standardjinvolute, 122, 124 
20° stub-tooth*form, 123, 125 
Gears, automobile’transmission, methods 
of holding,' 67, r 69, 70, 71, 74, 75, 76 
concentricity of,^88 


Gears, automobile transmission, correct 
center distances for, 88 
cutting accurate, 37, 66 
cutting high-grade, 1 
gaging and inspecting of, 88-92 
holding shank type on No. 64 Gear 
Shaper, 71, 73 

important points to remember in cut¬ 
ting, 90, 91, 92 

internal, calculating center distances of, 
112 

interference in, 110 

methods of holding shank type, 72, 74 
rules for calculating, 110-116 

Gears, measuring center distances of, 90, 
9i 

Gedrs, methods of holding automobile 
cluster, 74, 75, 76 

methods of holding on centers, 77, 78 
methods of using faceplate, work-arbor 
and work-supports, 68 
methods of holding in floating fixtures, 

79 

methods of testing concentricity of, 89 
necessity for accurate facing, 16 
necessity for having faces true with 
holes, 66 

properly shaped tooth curves for, 89 
resetting for recutting, 38 
roughing and finishing of,.35 
roughing and finishing on different 
machines, 35 

roughing and finishing on Gear Shaper, 

37 

shank, holding in floating fixtures, 71, 

73, 74 

showing methods of holding in floating 
fixtures, 79 

three essentials for quiet running, 88 

Gear Shaper, advisability of roughing and 
finishing gears on, 35 
care and maintenance of, 41 
important points on, 56 
clearance of gears cut on, 104 
control of helix angle on, 36 
directions for setting-up and operating 
3-34 

feeds for, 6 

instructions for oiling, 30, 31, 32 
names of principal parts, III 
No. 6, front view, II 
oiling of, 30, 31, 32 

order of setting-up operations, 3, 4, 5 

principles of operations, 1, 2 

production of, calculating, 94, 95, 96 

pulling over by hand, 33 

reduced travel of, 65 

setting for cutting internal gears, 116 

standard helical tooth, 118 


GEAR SHAPER—PINIONS 


05 


Gear Shaper, starting to operate, 32, 33 
stopping operation of, 34 
table of speeds, 15, 95 
time to load and remove work on, 96 
workholding fixtures for, 63-84 
Gear Shaper Cutter, angle on top face 
of spur, 57, 58 

centering with gear blank, 23, 26 
generating gear teeth with, 2 
group of, IV 

how accurately tested, 91 
methods of mounting, 4, 5, 24 
selecting and mounting, 4, 7 
setting for depth of cut, 28, 29 
setting to gear blanks, 19, 21 
setting to master gear, 29, 30 
sharpening of, 57 

on rotary surface grinder, 58, 59 
on universal grinder, 57, 58 
smallest number of teeth tor internal 
gears, 115 

Gear Shaper Helical Cutter, 60 

angular settings for sharpening, 58, 59, 
60, 61 

fixture for sharpening, 60, 61 
setting to gear blanks for stroke, 21,24, 

2 5 

sharpening ot, 58, 59, 60 
Grinding wheels for “dry” grinding, 61 
for “wet” grinding, 60 
Guides, adjusting of, on helical gear 
Shaper, 43, 44, 45 

adjusting of in spur Gear Shaper, 42 


Helical Gear tooth, Gear Shaper stand¬ 
ard for, 118 

Helical Gears, advantages of teeth on, 117 
definition of, 119, 120 
difference between normal and diam¬ 
etral plane, 120 
rules for calculating, 118, 119 
table of width of face of, 119 
width of face and helix angle for con¬ 
tinuous action, 118, 119 
Helix angle, Gear Shaper standard for, 
118 

necessity for obtaining correct, 36 
Helix control mechanism on Gear Shaper, 
36 

High-carbon and alloy steels, cutting oils 
for, 86 


Inches, conversion into millimeters, 128 
Indexing mechanisms, inaccurate, 35 
Index wheel, adjusting of worm to lower, 

? 3 > ?7 

adjusting of worm to upper, 41 
adjusting ring-gib to upper, 56 


Inspecting and gaging gears, 88-92 
important points on, 92 
Internal clutch gears, 114 
cut on Gear Shaper, n6 
limits for size of, 114 
limits tor backlash between teeth, 114 
smallest number of teeth cut in, 115 
Internal Gears, calculating elements of, 
110-116 

calculating inside diameter of, 113 
calculating involute base circle diame¬ 
ter of, 114 

formulas tor calculating, table of, 112 
interference of, no 
methods of holding, 80, 81, 82, 83 
setting apron-lever for cutting, 116 
smallest number of teeth cut with Gear 
Shaper cutter, 115 

Internal shank gears, methods of holding, 

7 2 , 74 

Involute base circle diameter, rules for 
calculating spur gears, 107 
rules for calculating internal gears, 113 


Lead screw nut, adjusting of, 48, 50 
Lever, apron, adjusting of tension on, 49, 


5 °, 5 2 . 

Line of action, definition ot, 107 
Location block for apron, adjusting of, 54 


IVIachinery steel, cutting oils for, 85 
Micarta, cutting of, 87 
Millimeters, conversion into inches, 129 
conversion of decimals of inches into, 
128 

Metric, table of tooth parts, 124, 125, 126 


Number of teeth, rules for calculating, 
105 


Oils for gear cutting, 85 
Outside diameter, rules for calculating, 
105 

Pinions, methods of holding transmis¬ 
sion in floating fixtures, 70, 72, 73, 74, 
77 , 78 

methods of holding internal in floating 
fixtures, 79, 80 

Pitch-dial, setting for depth of cut, 24, 27 
Pitch-dial, setting for stub tooth, 27 
“Pitch Gear,” relation of number of 
teeth in cutter to, 10 
Pitch point, definition of, 107 
Pressure angle, rule for calculating, 107 




PRODUCTION—YOKE-LEVER 


Production, calculation of, 39, 94 
example of calculating, 39, 95, 96 
formulas for calculating, 95, 96 
“Pull” and “push” strokes, cutting on. 65 


Ivack -clamp, adjustment of, 53, 54 
Rack-screw, adjusting of clamping nuts 
on, 52 , 53 

Ram, adjusting for length of stroke of, 
18, 22 

adjusting of taper gib on, 47, 48 
Rawhide, cutting of, 87 
Reduced travel, 65 

Relieving mechanism, setting of, 22, 26 
Resetting for recutting gears, 37, 38 
Ring-gib, adjusting to index wheel, 56 
Roll, adjusting eccentric backing off, 50, 
5i. 

Root diameter, rules for calculating, 106 
Roughing and finishing of gears, 35 
summary of important points on, 40 
Rules and formulas, 93-120 


Tables, gear tooth parts, standard invo¬ 
lute form, 122 

inches, decimals of, into millimeters, 128 
inches, fractions of, into millimeters, 

} 3 °> 131 

millimeters into inches, 129 
minimum width of face for continuous 
helical action, 119 

metric system, 20° stub-tooth form, 125 
standard involute form, 124 
rules for calculating diametral pitch 
gears, 98 

for internal gears, m 
strokes of Gear Shaper per minute, 15 
strokes per inch of pitch diameter of 
gear blank, 95 

Tangent, common, definition of, 108 
Teeth, number of, rules for calculating, 

106 

Thickness of tooth, rules for calculating, 
105 

chordal, rule for calculating, 107 
Tractor, internal drive gear, method of 
holding, 81 


Oection through cutter-spindle, 47 
through work-spindle, 8, 64 
Selecting change gears, 9 

work-arbors and supports, 11 
Soft steel, cutting oils for, 86 
Speeds for cutter sharpening, 61, 62 
for gear cutting, 20 

Spur cutter, setting to gear blanks for 
stroke, 21 

Starting lever, operating, 34 
Steel, alloy and high-carbon, cutting oils 
for, 86 

machinery, cutting oils for, 86 
Stroke, adjusting for length of, 18, 23 
Strokes, selection of, 20 


Tables, change gear chart, 6 
chordal tooth thickness, 100 
circular and diametral pitch, metric 
equivalent of, 126 
corrected addendum, 100 
decimal equivalents of fractions of an 
inch, 132 

gear tooth parts, 20° stub-tooth form, 
123 


Velocity, rule for calculating, 107 


Work , clamping, 14,15 

methods of supporting, 63-84 
removing from arbor, 34 
Work-arbor, mounting and testing, 13, 14 
necessity for hardening and grinding, 
66 

removing from work-spindle, 13 
testing for concentricity, 10, 13, T4 
Work-arbors and supports, selecting, 11 
Work-holding fixtures for Gear Shaper, 

63-84 

Work-spindle, adjusting of, 55 
section through, 8, 64 
Work-supports and faceplates, 63 
Worm, adjusting to lower index wheel, 
13 , 17 

adjusting to upper index wheel, 41, 42 


Yoke -lever, position when back gears 
are out, 15, 16 

position when back gears are in, 15, 17 


VERMONT PRINTING COMPANY, BRATTLEBORO 







Front View of No. 65 Fellows Helical Gear Shaper 
























































































































































































































































































































































































































































































































